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[null,null,null,null,null,null,null,null,null,"scemicircle","to the left",false]
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[null,null,null,null,null,null,null,null,null,10,{"$f":"\"ANGLE OF SINGLE RAY =\"&TEXT(A57/10,\"0,00\")","v":"ANGLE OF SINGLE RAY =34,00"},null,"SINGLE  RAY","TO CHANGE THE DIRECTION OF THE SEMICIRCLE MOVE THE SLIDER"]
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[null,null,null,null,null,null,null,null,null,null,"show rays",{"$f":"TRUE","v":true},"show rays",{"$f":"IF(circle_right,\"semicircle to the right\",\"semicircle to the left\")","v":"semicircle to the left"}]
[null,null,null,null,null,null,null,null,null,"table of values","Index n=",1.5]
[null,null,null,null,null,null,null,null,null,"ANGLE OF INCIDENT RAY ON THE RIGHT SIDE WITH HORIZONTAL  AXIS","EXPECTED ANGLE OF EMERGING RAY WITH THE HORIZONTAL AXIS","MEASURED ANGLE OF THE EMERGING RAY WITH THE HORIZONTAL AXIS","MEASURED INDEX OF REFRACTION",null,1]
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[null,null,null,null,null,null,null,null,null,20,13.180142161400394,{"$f":"CALC_POINT!F205","v":10.719321818403325},{"$f":"IF(circle_left,SIN(RADIANS(J11))/SIN(RADIANS(L11)),SIN(RADIANS(L11))/SIN(RADIANS(J11)))","v":1.8388380370343791}]
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[null,null,null,null,null,null,null,null,null,40,25.373993939179407,{"$f":"CALC_POINT!J205","v":22.941171901925284},{"$f":"IF(circle_left,SIN(RADIANS(J13))/SIN(RADIANS(L13)),IF((J13)<VALUE(MEASURED_CRITICAL),SIN(RADIANS(L13))/SIN(RADIANS(J13)),\"\"))","v":1.6490790837306901}]
[null,null,null,null,null,null,null,null,null,50,30.710220766102182,{"$f":"CALC_POINT!L205","v":28.261537375170427},{"$f":"IF(circle_left,SIN(RADIANS(J14))/SIN(RADIANS(L14)),IF((J14)<VALUE(MEASURED_CRITICAL),SIN(RADIANS(L14))/SIN(RADIANS(J14)),\"\"))","v":1.6178442126023913}]
[null,null,null,null,null,null,null,null,null,59.999999999999993,35.264389682754654,{"$f":"CALC_POINT!N205","v":32.746565615245579},{"$f":"IF(circle_left,SIN(RADIANS(J15))/SIN(RADIANS(L15)),IF((J15)<VALUE(MEASURED_CRITICAL),SIN(RADIANS(L15))/SIN(RADIANS(J15)),\"\"))","v":1.601011069718927}]
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[null,null,null,null,null,null,null,null,null,80,41.036410525203351,{"$f":"CALC_POINT!R205","v":38.016725813748941},{"$f":"IF(circle_left,SIN(RADIANS(J17))/SIN(RADIANS(L17)),IF((J17)<VALUE(MEASURED_CRITICAL),SIN(RADIANS(L17))/SIN(RADIANS(J17)),\"\"))","v":1.5989955634064446}]
[null,null,null,null,null,null,null,null,null,{"$f":"THETA","v":34},{"$f":"IF(circle_left,DEGREES(ASIN(SIN(RADIANS(THETA))/nn)),IF(J18<DEGREES(critical_angle),DEGREES(ASIN(nn*SIN(RADIANS(J18)))),\"total REFLECTION\"))","v":21.888112388828045},{"$f":"CALC_POINT!U205","v":19.45067848513732},{"$f":"IF(circle_left,SIN(RADIANS(J18))/SIN(RADIANS(L18)),IF((J18)<VALUE(MEASURED_CRITICAL),SIN(RADIANS(L18))/SIN(RADIANS(THETA)),\"\"))","v":1.6792817287383801}]
[null,null,null,null,null,null,null,null,null,null,null,"AVERAGE FROM MEASURED INDEX",null,"EXTIMATED FROM LEAST SQUARE FIT"]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AVERAGE(M9:M17)","v":1.9915165624178743}]
[null,null,null,null,null,807386475.11018872,null,null,null,null,"estimated from",{"$f":"X121","v":"least square fit, n = 1,63"}]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(circle_right, \"EXPECTED CRITICAL ANGLE\",\"NO CRITICAL ANGLE\")","v":"NO CRITICAL ANGLE"},{"$f":"IF(circle_right,TEXT(DEGREES(ASIN(1/nn)),\"0,00\"),\"NO CRITICAL ANGLE\")","v":"NO CRITICAL ANGLE"}]
[null,null,null,null,null,null,null,null,null,"measured critical angle",{"$f":"IF(circle_right,TEXT(CALC_POINT!AA203,\"0,00\"),\"NO CRITICAL ANGLE\")","v":"NO CRITICAL ANGLE"},{"$f":"IF(circle_right,1/SIN(RADIANS(K23)),\"\")","v":""},{"$f":"IF(circle_right,\"MEASURED INDEX FROM CRITICAL ANGLE\",\"\")","v":""}]
[]
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[]
[null,null,null,"_"]
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[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,{"$f":"\"ANGLE ON THE RIGHT SIDE WJCH WILL BE CONSIDERED  AS THE \"","v":"ANGLE ON THE RIGHT SIDE WJCH WILL BE CONSIDERED  AS THE "},null,{"$f":"\"ANGLE ON THE LEFT SIDE WHICH WILL BE CONSIDERED AS THE \"","v":"ANGLE ON THE LEFT SIDE WHICH WILL BE CONSIDERED AS THE "}]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(circle_left,\"ANGLE OF INCIDENCE\",\"ANGLE OF REFRACTION\")","v":"ANGLE OF INCIDENCE"},null,{"$f":"IF(circle_left,\"ANGLE OF REFACTION\",\"ANGLE OF INCIDENCE\")","v":"ANGLE OF REFACTION"}]
[null,null,null,null,null,null,null,null,null,{"$f":"J33&J34","v":"ANGLE ON THE RIGHT SIDE WJCH WILL BE CONSIDERED  AS THE ANGLE OF INCIDENCE"}]
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[340,null,null,null,null,null,null,{"$f":"A57/10","v":34}]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"RADIANS(U75)","v":0},{"$f":"RADIANS(V75)","v":0},{"$f":"RADIANS(W75)","v":0},{"$f":"RADIANS(X75)","v":0},{"$f":"RADIANS(Y75)","v":0}]
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[null,null,null,0,145,{"$f":"\"Point at  \"& X_SOURCE & \" , \" & y_SOURCE","v":"Point at  204 , 26"},null,null,null,null,null,"RADIUS A POIN 1=",null,"gonia_1",{"$f":"PI()/2-A_GONIA+OMEGA","v":1.5523019415015511},{"$f":"RADIUS_OF_SEMICIRCLE*COS(O8)","v":1.3869998250801059},{"$f":"RADIUS_OF_SEMICIRCLE*SIN(O8)","v":74.987173779822015},{"$f":"-ATAN(Q8/P8)","v":-1.5523019415015511},null,null,"XSR","YSR",null,null,null,"x^2(1+k^2)+2*X*k(Y11-X11*K)+(Y11-X11*k)^2-R^2    K=TAN(KLISI)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"rot+transposed",{"$f":"(BG7-XC)*COS(radiansg)-(BH7-YC)*SIN(radiansg)","v":199.35467295328164},{"$f":"(BG7-XC)*SIN(radiansg)+(BH7-YC)*COS(radiansg)","v":21.970761745786632},{"$f":"(BI7-XC)*COS(radiansg)-(BJ7-YC)*SIN(radiansg)","v":199.42447194668662},{"$f":"(BI7-XC)*SIN(radiansg)+(BJ7-YC)*COS(radiansg)","v":19.971980091748438},{"$f":"(BK7-XC)*COS(radiansg)-(BL7-YC)*SIN(radiansg)","v":199.49427094009164},{"$f":"(BK7-XC)*SIN(radiansg)+(BL7-YC)*COS(radiansg)","v":17.973198437710248},{"$f":"(BM7-XC)*COS(radiansg)-(BN7-YC)*SIN(radiansg)","v":199.56406993349663},{"$f":"(BM7-XC)*SIN(radiansg)+(BN7-YC)*COS(radiansg)","v":15.974416783672055},{"$f":"(BO7-XC)*COS(radiansg)-(BP7-YC)*SIN(radiansg)","v":199.63386892690164},{"$f":"(BO7-XC)*SIN(radiansg)+(BP7-YC)*COS(radiansg)","v":13.975635129633865},{"$f":"(BQ7-XC)*COS(radiansg)-(BR7-YC)*SIN(radiansg)","v":199.70366792030663},{"$f":"(BQ7-XC)*SIN(radiansg)+(BR7-YC)*COS(radiansg)","v":11.976853475595671},{"$f":"(BS7-XC)*COS(radiansg)-(BT7-YC)*SIN(radiansg)","v":199.77346691371164},{"$f":"(BS7-XC)*SIN(radiansg)+(BT7-YC)*COS(radiansg)","v":9.9780718215574815},{"$f":"(BU7-XC)*COS(radiansg)-(BV7-YC)*SIN(radiansg)","v":199.84326590711663},{"$f":"(BU7-XC)*SIN(radiansg)+(BV7-YC)*COS(radiansg)","v":7.9792901675192898},{"$f":"(BW7-XC)*COS(radiansg)-(BX7-YC)*SIN(radiansg)","v":199.91306490052165},{"$f":"(BW7-XC)*SIN(radiansg)+(BX7-YC)*COS(radiansg)","v":5.980508513481098},{"$f":"(BY7-XC)*COS(radiansg)-(BZ7-YC)*SIN(radiansg)","v":199.98286389392663},{"$f":"(BY7-XC)*SIN(radiansg)+(BZ7-YC)*COS(radiansg)","v":3.9817268594429067},{"$f":"(CA7-XC)*COS(radiansg)-(CB7-YC)*SIN(radiansg)","v":200.05266288733165},{"$f":"(CA7-XC)*SIN(radiansg)+(CB7-YC)*COS(radiansg)","v":1.9829452054047154},{"$f":"(CC7-XC)*COS(radiansg)-(CD7-YC)*SIN(radiansg)","v":200.12246188073664},{"$f":"(CC7-XC)*SIN(radiansg)+(CD7-YC)*COS(radiansg)","v":-1.583644863347633E-2},{"$f":"(CE7-XC)*COS(radiansg)-(CF7-YC)*SIN(radiansg)","v":200.19226087414165},{"$f":"(CE7-XC)*SIN(radiansg)+(CF7-YC)*COS(radiansg)","v":-2.0146181026716681},{"$f":"(CG7-XC)*COS(radiansg)-(CH7-YC)*SIN(radiansg)","v":200.26205986754664},{"$f":"(CG7-XC)*SIN(radiansg)+(CH7-YC)*COS(radiansg)","v":-4.0133997567098598},{"$f":"(CI7-XC)*COS(radiansg)-(CJ7-YC)*SIN(radiansg)","v":200.33185886095166},{"$f":"(CI7-XC)*SIN(radiansg)+(CJ7-YC)*COS(radiansg)","v":-6.0121814107480516},{"$f":"(CK7-XC)*COS(radiansg)-(CL7-YC)*SIN(radiansg)","v":200.40165785435664},{"$f":"(CK7-XC)*SIN(radiansg)+(CL7-YC)*COS(radiansg)","v":-8.0109630647862424},"rot+transposed"]
["Calculstion of max angle",null,null,null,"Second: ROTATION at angle g: ",null,null,null,null,null,null,"RADIUS AT POINT 2",null,"gonia_2",{"$f":"-O6+ABS(O7)","v":-1.2289537012190539},{"$f":"RADIUS_OF_SEMICIRCLE*COS(O9)","v":25.141775165791163},{"$f":"RADIUS_OF_SEMICIRCLE*SIN(O9)","v":-70.660393018386245},{"$f":"-ATAN(Q9/P9)","v":1.2289537012190539},null,null,null,"KLISI_F = -(A_GONIA - dgon * I - omeGA)",null,null,null,"X=(-K*(Y11-X11*K)+SQRT(R^2*(1+K^2)-(Y11-X11*K)^2))/(1+K^)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CUT OF CIRCLE",{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BH8-TAN(KLISI_PAR)*BG8)^2","v":5406.5850847662377},{"$f":"BG9","v":5406.5850847662377},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BJ8-TAN(KLISI_PAR)*BI8)^2","v":5462.653374534184},{"$f":"BI9","v":5462.653374534184},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BL8-TAN(KLISI_PAR)*BK8)^2","v":5510.711908620995},{"$f":"BK9","v":5510.711908620995},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BN8-TAN(KLISI_PAR)*BM8)^2","v":5550.76068702667},{"$f":"BM9","v":5550.76068702667},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BP8-TAN(KLISI_PAR)*BO8)^2","v":5582.7997097512107},{"$f":"BO9","v":5582.7997097512107},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BR8-TAN(KLISI_PAR)*BQ8)^2","v":5606.8289767946162},{"$f":"BQ9","v":5606.8289767946162},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BT8-TAN(KLISI_PAR)*BS8)^2","v":5622.8484881568866},{"$f":"BS9","v":5622.8484881568866},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BV8-TAN(KLISI_PAR)*BU8)^2","v":5630.8582438380217},{"$f":"BU9","v":5630.8582438380217},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BX8-TAN(KLISI_PAR)*BW8)^2","v":5630.8582438380217},{"$f":"BW9","v":5630.8582438380217},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(BZ8-TAN(KLISI_PAR)*BY8)^2","v":5622.8484881568866},{"$f":"BY9","v":5622.8484881568866},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(CB8-TAN(KLISI_PAR)*CA8)^2","v":5606.8289767946162},{"$f":"CA9","v":5606.8289767946162},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(CD8-TAN(KLISI_PAR)*CC8)^2","v":5582.7997097512107},{"$f":"CC9","v":5582.7997097512107},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(CF8-TAN(KLISI_PAR)*CE8)^2","v":5550.76068702667},{"$f":"CE9","v":5550.76068702667},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(CH8-TAN(KLISI_PAR)*CG8)^2","v":5510.711908620995},{"$f":"CG9","v":5510.711908620995},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(CJ8-TAN(KLISI_PAR)*CI8)^2","v":5462.653374534184},{"$f":"CI9","v":5462.653374534184},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+TAN(KLISI_PAR)^2)-(CL8-TAN(KLISI_PAR)*CK8)^2","v":5406.5850847662377},{"$f":"CK9","v":5406.5850847662377},"CUT OF CIRCLE"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"anoigma",{"$f":"GONIA_1-GONIA_2","v":2.781255642720605},null,null,null,null,null,null,null,null,null,null,{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+Z6^2)-(YSR-XSR*Z6)^2","v":4602.3477724336599},4602.3477724336599,4895.2833106101416,4895.2833106101416,5147.4636587346231,5147.4636587346231,5358.9342611255915,5358.9342611255915,5529.5499215692917,5529.5499215692917,5658.9713886538802,5658.9713886538802,null,5746.659962106758,5746.659962106758,5791.8700142613643,5791.8700142613643,5793.639282806701,5793.639282806701,5750.7767489546886,5750.7767489546886,5661.8478678664296,5661.8478678664296,5525.1568641653284,5525.1568641653284,5338.7257429154233,5338.7257429154233,5100.269593485853,5100.269593485853,4807.1676777336534,null,null,"X2,Y2",{"$f":"IF(BH8+TAN(KLISI_PAR)*(0-BG8)>RADIUS_OF_SEMICIRCLE,IF(BG9>0,(-TAN(KLISI_PAR)*(BH8-TAN(KLISI_PAR)*BG8)+SQRT(BG9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BH8+TAN(KLISI_PAR)*(BG10-BG8)","v":15.009143164482328},{"$f":"IF(BJ8+TAN(KLISI_PAR)*(0-BI8)>RADIUS_OF_SEMICIRCLE,IF(BI9>0,(-TAN(KLISI_PAR)*(BJ8-TAN(KLISI_PAR)*BI8)+SQRT(BI9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BJ8+TAN(KLISI_PAR)*(BI10-BI8)","v":13.007924075884684},{"$f":"IF(BL8+TAN(KLISI_PAR)*(0-BK8)>RADIUS_OF_SEMICIRCLE,IF(BK9>0,(-TAN(KLISI_PAR)*(BL8-TAN(KLISI_PAR)*BK8)+SQRT(BK9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BL8+TAN(KLISI_PAR)*(BK10-BK8)","v":11.006704987287041},{"$f":"IF(BN8+TAN(KLISI_PAR)*(0-BM8)>RADIUS_OF_SEMICIRCLE,IF(BM9>0,(-TAN(KLISI_PAR)*(BN8-TAN(KLISI_PAR)*BM8)+SQRT(BM9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BN8+TAN(KLISI_PAR)*(BM10-BM8)","v":9.0054858986893969},{"$f":"IF(BP8+TAN(KLISI_PAR)*(0-BO8)>RADIUS_OF_SEMICIRCLE,IF(BO9>0,(-TAN(KLISI_PAR)*(BP8-TAN(KLISI_PAR)*BO8)+SQRT(BO9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BP8+TAN(KLISI_PAR)*(BO10-BO8)","v":7.0042668100917531},{"$f":"IF(BR8+TAN(KLISI_PAR)*(0-BQ8)>RADIUS_OF_SEMICIRCLE,IF(BQ9>0,(-TAN(KLISI_PAR)*(BR8-TAN(KLISI_PAR)*BQ8)+SQRT(BQ9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BR8+TAN(KLISI_PAR)*(BQ10-BQ8)","v":5.0030477214941076},{"$f":"IF(BT8+TAN(KLISI_PAR)*(0-BS8)>RADIUS_OF_SEMICIRCLE,IF(BS9>0,(-TAN(KLISI_PAR)*(BT8-TAN(KLISI_PAR)*BS8)+SQRT(BS9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BT8+TAN(KLISI_PAR)*(BS10-BS8)","v":3.0018286328964656},{"$f":"IF(BV8+TAN(KLISI_PAR)*(0-BU8)>RADIUS_OF_SEMICIRCLE,IF(BU9>0,(-TAN(KLISI_PAR)*(BV8-TAN(KLISI_PAR)*BU8)+SQRT(BU9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BV8+TAN(KLISI_PAR)*(BU10-BU8)","v":1.0006095442988219},{"$f":"IF(BX8+TAN(KLISI_PAR)*(0-BW8)>RADIUS_OF_SEMICIRCLE,IF(BW9>0,(-TAN(KLISI_PAR)*(BX8-TAN(KLISI_PAR)*BW8)+SQRT(BW9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BX8+TAN(KLISI_PAR)*(BW10-BW8)","v":-1.0006095442988219},{"$f":"IF(BZ8+TAN(KLISI_PAR)*(0-BY8)>RADIUS_OF_SEMICIRCLE,IF(BY9>0,(-TAN(KLISI_PAR)*(BZ8-TAN(KLISI_PAR)*BY8)+SQRT(BY9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"BZ8+TAN(KLISI_PAR)*(BY10-BY8)","v":-3.0018286328964652},{"$f":"IF(CB8+TAN(KLISI_PAR)*(0-CA8)>RADIUS_OF_SEMICIRCLE,IF(CA9>0,(-TAN(KLISI_PAR)*(CB8-TAN(KLISI_PAR)*CA8)+SQRT(CA9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"CB8+TAN(KLISI_PAR)*(CA10-CA8)","v":-5.0030477214941094},{"$f":"IF(CD8+TAN(KLISI_PAR)*(0-CC8)>RADIUS_OF_SEMICIRCLE,IF(CC9>0,(-TAN(KLISI_PAR)*(CD8-TAN(KLISI_PAR)*CC8)+SQRT(CC9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"CD8+TAN(KLISI_PAR)*(CC10-CC8)","v":-7.0042668100917522},{"$f":"IF(CF8+TAN(KLISI_PAR)*(0-CE8)>RADIUS_OF_SEMICIRCLE,IF(CE9>0,(-TAN(KLISI_PAR)*(CF8-TAN(KLISI_PAR)*CE8)+SQRT(CE9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"CF8+TAN(KLISI_PAR)*(CE10-CE8)","v":-9.0054858986893969},{"$f":"IF(CH8+TAN(KLISI_PAR)*(0-CG8)>RADIUS_OF_SEMICIRCLE,IF(CG9>0,(-TAN(KLISI_PAR)*(CH8-TAN(KLISI_PAR)*CG8)+SQRT(CG9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"CH8+TAN(KLISI_PAR)*(CG10-CG8)","v":-11.006704987287041},{"$f":"IF(CJ8+TAN(KLISI_PAR)*(0-CI8)>RADIUS_OF_SEMICIRCLE,IF(CI9>0,(-TAN(KLISI_PAR)*(CJ8-TAN(KLISI_PAR)*CI8)+SQRT(CI9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"CJ8+TAN(KLISI_PAR)*(CI10-CI8)","v":-13.007924075884684},{"$f":"IF(CL8+TAN(KLISI_PAR)*(0-CK8)>RADIUS_OF_SEMICIRCLE,IF(CK9>0,(-TAN(KLISI_PAR)*(CL8-TAN(KLISI_PAR)*CK8)+SQRT(CK9))/(1+TAN(KLISI_PAR)^2),0),0)","v":0},{"$f":"CL8+TAN(KLISI_PAR)*(CK10-CK8)","v":-15.009143164482326},"X2,Y2"]
["We transforn to a reference frame",null,null,null,"x11=x1cosg-y1singy11=x1sing+y1cosg",null,null,null,null,null,null,null,null,"DGON",{"$f":"(2*A_GONIA)/15","v":2.4022467391279199E-2},{"$f":"2*A_GONIA/15","v":2.4022467391279199E-2},null,null,null,"incidence",null,null,null,null,"X2,Y2",{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+Z6^2)-(YSR-XSR*Z6)^2>0,(-Z6*(YSR-XSR*Z6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+Z6^2)-(YSR-XSR*Z6)^2))/(1+Z6^2),XSR)","v":67.661739035780315},{"$f":"IF(Z11<>X_SOURCE,YSR+AA6*(Z11-XSR),YSR)","v":32.355665201846257},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AB6^2)-(YSR-XSR*AB6)^2>0,(-AB6*(YSR-XSR*AB6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AB6^2)-(YSR-XSR*AB6)^2))/(1+AB6^2),XSR)","v":69.104747556993388},{"$f":"IF(AB11<>X_SOURCE,YSR+AC6*(AB11-XSR),YSR)","v":29.14676423008596},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AD6^2)-(YSR-XSR*AD6)^2>0,(-AD6*(YSR-XSR*AD6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AD6^2)-(YSR-XSR*AD6)^2))/(1+AD6^2),XSR)","v":70.352012645558901},{"$f":"IF(AD11<>X_SOURCE,YSR+AE6*(AD11-XSR),YSR)","v":25.992197227612785},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AF6^2)-(YSR-XSR*AF6)^2>0,(-AF6*(YSR-XSR*AF6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AF6^2)-(YSR-XSR*AF6)^2))/(1+AF6^2),XSR)","v":71.426093519051847},{"$f":"IF(AF11<>X_SOURCE,YSR+AG6*(AF11-XSR),YSR)","v":22.876039093506943},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AH6^2)-(YSR-XSR*AH6)^2>0,(-AH6*(YSR-XSR*AH6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AH6^2)-(YSR-XSR*AH6)^2))/(1+AH6^2),XSR)","v":72.343589360386389},{"$f":"IF(AH11<>X_SOURCE,YSR+AI6*(AH11-XSR),YSR)","v":19.783960130767319},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AJ6^2)-(YSR-XSR*AJ6)^2>0,(-AJ6*(YSR-XSR*AJ6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AJ6^2)-(YSR-XSR*AJ6)^2))/(1+AJ6^2),XSR)","v":73.116497536790021},{"$f":"IF(AJ11<>X_SOURCE,YSR+AK6*(AJ11-XSR),YSR)","v":16.702628175008179},null,{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AM6^2)-(YSR-XSR*AM6)^2>0,(-AM6*(YSR-XSR*AM6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AM6^2)-(YSR-XSR*AM6)^2))/(1+AM6^2),XSR)","v":73.753077548874487},{"$f":"IF(AM11<>X_SOURCE,YSR+AN6*(AM11-XSR),YSR)","v":13.619234635973612},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AO6^2)-(YSR-XSR*AO6)^2>0,(-AO6*(YSR-XSR*AO6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AO6^2)-(YSR-XSR*AO6)^2))/(1+AO6^2),XSR)","v":74.258378387598768},{"$f":"IF(AO11<>X_SOURCE,YSR+AP6*(AO11-XSR),YSR)","v":10.52108545940975},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AQ6^2)-(YSR-XSR*AQ6)^2>0,(-AQ6*(YSR-XSR*AQ6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AQ6^2)-(YSR-XSR*AQ6)^2))/(1+AQ6^2),XSR)","v":74.634514851206475},{"$f":"IF(AQ11<>X_SOURCE,YSR+AR6*(AQ11-XSR),YSR)","v":7.3952141906127906},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AS6^2)-(YSR-XSR*AS6)^2>0,(-AS6*(YSR-XSR*AS6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AS6^2)-(YSR-XSR*AS6)^2))/(1+AS6^2),XSR)","v":74.88073305096853},{"$f":"IF(AS11<>X_SOURCE,YSR+AT6*(AS11-XSR),YSR)","v":4.2279803393097382},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AU6^2)-(YSR-XSR*AU6)^2>0,(-AU6*(YSR-XSR*AU6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AU6^2)-(YSR-XSR*AU6)^2))/(1+AU6^2),XSR)","v":74.993271360230722},{"$f":"IF(AU11<>X_SOURCE,YSR+AV6*(AU11-XSR),YSR)","v":1.0046146976811769},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AW6^2)-(YSR-XSR*AW6)^2>0,(-AW6*(YSR-XSR*AW6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AW6^2)-(YSR-XSR*AW6)^2))/(1+AW6^2),XSR)","v":74.964990355773239},{"$f":"IF(AW11<>X_SOURCE,YSR+AX6*(AW11-XSR),YSR)","v":-2.2913360641391947},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+AY6^2)-(YSR-XSR*AY6)^2>0,(-AY6*(YSR-XSR*AY6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+AY6^2)-(YSR-XSR*AY6)^2))/(1+AY6^2),XSR)","v":74.784704238317431},{"$f":"IF(AY11<>X_SOURCE,YSR+AZ6*(AY11-XSR),YSR)","v":-5.6787333083518732},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+BA6^2)-(YSR-XSR*BA6)^2>0,(-BA6*(YSR-XSR*BA6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+BA6^2)-(YSR-XSR*BA6)^2))/(1+BA6^2),XSR)","v":74.436082970187869},{"$f":"IF(BA11<>X_SOURCE,YSR+BB6*(BA11-XSR),YSR)","v":-9.1798448818761287},{"$f":"IF(RADIUS_OF_SEMICIRCLE^2*(1+BC6^2)-(YSR-XSR*BC6)^2>0,(-BC6*(YSR-XSR*BC6)+SQRT(RADIUS_OF_SEMICIRCLE^2*(1+BC6^2)-(YSR-XSR*BC6)^2))/(1+BC6^2),XSR)","v":73.895883031327969},{"$f":"IF(BC11<>X_SOURCE,YSR+BD6*(BC11-XSR),YSR)","v":-12.821796715760833},"in or out of circle","true =in",null,{"$f":"IF(ABS(BH10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(BJ10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(BL10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(BN10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(BP10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(BR10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(BT10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(BV10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(BX10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(BZ10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(CB10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(CD10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(CF10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(CH10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(CJ10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},null,{"$f":"IF(ABS(CL10)<RADIUS_OF_SEMICIRCLE,TRUE,FALSE)","v":true},"true =in"]
["where the center of the cirlce is at 0,0",null,null,null,"x11",{"$f":"B16*COS(radiansg)-B18*SIN(radiansg)","v":202.9683417976305},null,null,null,null,"KLISI_F = -(A_GONIA - dgon * I - omeGA)",null,null,null,null,null,null,null,null,"in degrees",null,null,null,null,"INCID = Atn(ykyklos / xkyklos) - agoN(I)",{"$f":"ATAN(AA11/Z11)-Z5","v":0.44052578122191016},{"$f":"Z12","v":0.44052578122191016},{"$f":"ATAN(AC11/AB11)-AB5","v":0.3695866689961268},{"$f":"AB12","v":0.3695866689961268},{"$f":"ATAN(AE11/AD11)-AD5","v":0.30033112552188879},{"$f":"AD12","v":0.30033112552188879},{"$f":"ATAN(AG11/AF11)-AF5","v":0.23235749278635487},{"$f":"AF12","v":0.23235749278635487},{"$f":"ATAN(AI11/AH11)-AH5","v":0.16532731643379017},{"$f":"AH12","v":0.16532731643379017},{"$f":"ATAN(AK11/AJ11)-AJ5","v":9.8944484137932581E-2},{"$f":"AJ12","v":9.8944484137932581E-2},null,{"$f":"ATAN(AN11/AM11)-AM5","v":3.2939997623981421E-2},{"$f":"AM12","v":3.2939997623981421E-2},{"$f":"ATAN(AP11/AO11)-AO5","v":-3.293999762398131E-2},{"$f":"AO12","v":-3.293999762398131E-2},{"$f":"ATAN(AR11/AQ11)-AQ5","v":-9.8944484137932581E-2},{"$f":"AQ12","v":-9.8944484137932581E-2},{"$f":"ATAN(AT11/AS11)-AS5","v":-0.16532731643379012},{"$f":"AS12","v":-0.16532731643379012},{"$f":"ATAN(AV11/AU11)-AU5","v":-0.23235749278635481},{"$f":"AU12","v":-0.23235749278635481},{"$f":"ATAN(AX11/AW11)-AW5","v":-0.30033112552188879},{"$f":"AW12","v":-0.30033112552188879},{"$f":"ATAN(AZ11/AY11)-AY5","v":-0.3695866689961268},{"$f":"AY12","v":-0.3695866689961268},{"$f":"ATAN(BB11/BA11)-BA5","v":-0.44052578122191033},{"$f":"BA12","v":-0.44052578122191033},{"$f":"ATAN(BD11/BC11)-BC5","v":-0.51364380588102077},{"$f":"BC12","v":-0.51364380588102077},null,null,null,{"$f":"IF(BG12<>0,BH8+TAN(radiansg+ANGLE_p_R)*(BG12-BG8),BG8+(0-BG8)*TAN(radiansg+ANGLE_p_R))","v":192.39305437197734},null,{"$f":"IF(BI12<>0,BJ8+TAN(radiansg+ANGLE_p_R)*(BI12-BI8),BI8+(0-BI8)*TAN(radiansg+ANGLE_p_R))","v":192.46041593082288},null,{"$f":"IF(BK12<>0,BL8+TAN(radiansg+ANGLE_p_R)*(BK12-BK8),BK8+(0-BK8)*TAN(radiansg+ANGLE_p_R))","v":192.52777748966844},null,{"$f":"IF(BM12<>0,BN8+TAN(radiansg+ANGLE_p_R)*(BM12-BM8),BM8+(0-BM8)*TAN(radiansg+ANGLE_p_R))","v":192.59513904851397},null,{"$f":"IF(BO12<>0,BP8+TAN(radiansg+ANGLE_p_R)*(BO12-BO8),BO8+(0-BO8)*TAN(radiansg+ANGLE_p_R))","v":192.66250060735953},null,{"$f":"IF(BQ12<>0,BR8+TAN(radiansg+ANGLE_p_R)*(BQ12-BQ8),BR8+(0-BQ8)*TAN(radiansg+ANGLE_p_R))","v":5.0030477214941076},null,{"$f":"IF(BS10<>0,BT8+TAN(radiansg+ANGLE_p_R)*(BS12-BS8),BT8+(0-BS8)*TAN(radiansg+ANGLE_p_R))","v":3.0018286328964656},null,{"$f":"IF(BU10<>0,BV8+TAN(radiansg+ANGLE_p_R)*(BU12-BU8),BV8+(0-BU8)*TAN(radiansg+ANGLE_p_R))","v":1.0006095442988219},null,{"$f":"IF(BW10<>0,BX8+TAN(radiansg+ANGLE_p_R)*(BW12-BW8),BX8+(0-BW8)*TAN(radiansg+ANGLE_p_R))","v":-1.0006095442988219},null,{"$f":"IF(BY10<>0,BZ8+TAN(radiansg+ANGLE_p_R)*(BY12-BY8),BZ8+(0-BY8)*TAN(radiansg+ANGLE_p_R))","v":-3.0018286328964652},null,{"$f":"IF(CA10<>0,CB8+TAN(radiansg+ANGLE_p_R)*(CA12-CA8),CB8+(0-CA8)*TAN(radiansg+ANGLE_p_R))","v":-5.0030477214941094},null,{"$f":"IF(CC10<>0,CD8+TAN(radiansg+ANGLE_p_R)*(CC12-CC8),CD8+(0-CC8)*TAN(radiansg+ANGLE_p_R))","v":-7.0042668100917522},null,{"$f":"IF(CE10<>0,CF8+TAN(radiansg+ANGLE_p_R)*(CE12-CE8),CF8+(0-CE8)*TAN(radiansg+ANGLE_p_R))","v":-9.0054858986893969},null,{"$f":"IF(CG10<>0,CH8+TAN(radiansg+ANGLE_p_R)*(CG12-CG8),CH8+(0-CG8)*TAN(radiansg+ANGLE_p_R))","v":-11.006704987287041},null,{"$f":"IF(CI10<>0,CJ8+TAN(radiansg+ANGLE_p_R)*(CI12-CI8),CJ8+(0-CI8)*TAN(radiansg+ANGLE_p_R))","v":-13.007924075884684},null,{"$f":"IF(CK10<>0,CL8+TAN(radiansg+ANGLE_p_R)*(CK12-CK8),CL8+(0-CK8)*TAN(radiansg+ANGLE_p_R))","v":-15.009143164482326}]
["and the diameter is perpendicular to the",null,null,null,"y11 ",{"$f":"B16*SIN(radiansg)+B18*COS(radiansg)","v":33.10365882980669},null,null,null,null,null,null,null,null,null,{"$f":"P8*COS(radiansg)+Q8*SIN(radiansg)+XC","v":4.0031695263209137},null,null,null,"refraction",{"$f":"ATAN((V7-htry)/(U7-htrx))","v":0.15298222726926275},{"$f":"U13","v":0.15298222726926275},null,null,"REFRACTION",{"$f":"ASIN(SIN(Z12)/nn)","v":0.28825195786513635},{"$f":"Z13","v":0.28825195786513635},{"$f":"ASIN(SIN(AB12)/nn)","v":0.24321065550022744},{"$f":"AB13","v":0.24321065550022744},{"$f":"ASIN(SIN(AD12)/nn)","v":0.19852585087590924},{"$f":"AD13","v":0.19852585087590924},{"$f":"ASIN(SIN(AF12)/nn)","v":0.15412432808067061},{"$f":"AF13","v":0.15412432808067061},{"$f":"ASIN(SIN(AH12)/nn)","v":0.1099381207973459},{"$f":"AH13","v":0.1099381207973459},{"$f":"ASIN(SIN(AJ12)/nn)","v":6.5903107285128396E-2},{"$f":"AJ13","v":6.5903107285128396E-2},null,{"$f":"ASIN(SIN(AM12)/nn)","v":2.1957791802045858E-2},{"$f":"AM13","v":2.1957791802045858E-2},{"$f":"ASIN(SIN(AO12)/nn)","v":-2.1957791802045785E-2},{"$f":"AO13","v":-2.1957791802045785E-2},{"$f":"ASIN(SIN(AQ12)/nn)","v":-6.5903107285128396E-2},{"$f":"AQ13","v":-6.5903107285128396E-2},{"$f":"ASIN(SIN(AS12)/nn)","v":-0.10993812079734586},{"$f":"AS13","v":-0.10993812079734586},{"$f":"ASIN(SIN(AU12)/nn)","v":-0.15412432808067053},{"$f":"AU13","v":-0.15412432808067053},{"$f":"ASIN(SIN(AW12)/nn)","v":-0.19852585087590924},{"$f":"AW13","v":-0.19852585087590924},{"$f":"ASIN(SIN(AY12)/nn)","v":-0.24321065550022744},{"$f":"AY13","v":-0.24321065550022744},{"$f":"ASIN(SIN(BA12)/nn)","v":-0.28825195786513647},{"$f":"BA13","v":-0.28825195786513647},{"$f":"ASIN(SIN(BC12)/nn)","v":-0.33372989742387055},{"$f":"BC13","v":-0.33372989742387055},"ANGLE","INCIDENCE",{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BG13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BI13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BK13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BM13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BO13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BQ13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BS13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BU13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BW13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"BY13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"CA13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"CC13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"CE13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"CG13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"CI13","v":3.4906585039886591E-2},{"$f":"KLISI_PAR","v":3.4906585039886591E-2},{"$f":"CK13","v":3.4906585039886591E-2},"INCIDENCE"]
["x axis",null,null,null,"Disance of source from center =",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"in degrees",{"$f":"DEGREES(U13)","v":8.7652359630399292},{"$f":"DEGREES(V13)","v":8.7652359630399292},null,null,"NEW KLISI",{"$f":"ATAN(AA11/Z11)-Z13","v":0.15780190545470762},{"$f":"Z14","v":0.15780190545470762},{"$f":"ATAN(AC11/AB11)-AB13","v":0.15592656298511234},{"$f":"AB14","v":0.15592656298511234},{"$f":"ATAN(AE11/AD11)-AD13","v":0.15537829152647176},{"$f":"AD14","v":0.15537829152647176},{"$f":"ATAN(AG11/AF11)-AF13","v":0.15582864897745569},{"$f":"AF14","v":0.15582864897745569},{"$f":"ATAN(AI11/AH11)-AH13","v":0.15700714729949489},{"$f":"AH14","v":0.15700714729949489},{"$f":"ATAN(AK11/AJ11)-AJ13","v":0.15868179590713399},{"$f":"AJ14","v":0.15868179590713399},null,{"$f":"ATAN(AN11/AM11)-AM13","v":0.16064509226754459},{"$f":"AM14","v":0.16064509226754459},{"$f":"ATAN(AP11/AO11)-AO13","v":0.1627031480149527},{"$f":"AO14","v":0.1627031480149527},{"$f":"ATAN(AR11/AQ11)-AQ13","v":0.16466644437536321},{"$f":"AQ14","v":0.16466644437536321},{"$f":"ATAN(AT11/AS11)-AS13","v":0.16634109298300234},{"$f":"AS14","v":0.16634109298300234},{"$f":"ATAN(AV11/AU11)-AU13","v":0.16751959130504152},{"$f":"AU14","v":0.16751959130504152},{"$f":"ATAN(AX11/AW11)-AW13","v":0.16796994875602544},{"$f":"AW14","v":0.16796994875602544},{"$f":"ATAN(AZ11/AY11)-AY13","v":0.16742167729738483},{"$f":"AY14","v":0.16742167729738483},{"$f":"ATAN(BB11/BA11)-BA13","v":0.16554633482778958},{"$f":"BA14","v":0.16554633482778958},{"$f":"ATAN(BD11/BC11)-BC13","v":0.16192871711869233},{"$f":"BC14","v":0.16192871711869233},null,"refraction",{"$f":"ASIN(SIN(BG13)/nn)","v":2.3268430743283157E-2},{"$f":"ASIN(SIN(BH13)/nn)","v":2.3268430743283157E-2},{"$f":"ASIN(SIN(BI13)/nn)","v":2.3268430743283157E-2},2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,{"$f":"ASIN(SIN(BY13)/nn)","v":2.3268430743283157E-2},2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,2.3268430743283157E-2,"refraction"]
["First","X1=X-XC  Y1=Y-YC",null,null,"rho=",{"$f":"SQRT(F12^2+F13^2)","v":205.65018842685265},null,null,null,null,null,null,null,null,null,null,null,null,null,"X2,Y2",{"$f":"ASIN(SIN(U13)/nn)","v":0.10176636691864138},{"$f":"ASIN(SIN(V13)/nn)","v":0.10176636691864138},null,null,"X3,Y3",{"$f":"IF(Z11<>XSR,0,XSR)","v":0},{"$f":"IF(Z11<>XSR,AA11+TAN(AA14)*(Z15-Z11),YSR)","v":21.588996620436106},{"$f":"IF(AB11<>XSR,0,XSR)","v":0},{"$f":"IF(AB11<>XSR,AC11+TAN(AC14)*(AB15-AB11),YSR)","v":18.283314064258931},{"$f":"IF(AD11<>XSR,0,XSR)","v":0},{"$f":"IF(AD11<>XSR,AE11+TAN(AE14)*(AD15-AD11),YSR)","v":14.97219548712196},{"$f":"IF(AF11<>XSR,0,XSR)","v":0},{"$f":"IF(AF11<>XSR,AG11+TAN(AG14)*(AF15-AF11),YSR)","v":11.654833502345014},{"$f":"IF(AH11<>XSR,0,XSR)","v":0},{"$f":"IF(AH11<>XSR,AI11+TAN(AI14)*(AH15-AH11),YSR)","v":8.3312365550671128},{"$f":"IF(AJ11<>XSR,0,XSR)","v":0},{"$f":"IF(AJ11<>XSR,AK11+TAN(AK14)*(AJ15-AJ11),YSR)","v":5.0019988425977466},null,{"$f":"IF(AM11<>XSR,0,XSR)","v":0},{"$f":"IF(AM11<>XSR,AN11+TAN(AN14)*(AM15-AM11),YSR)","v":1.6681810466088098},{"$f":"IF(AO11<>XSR,0,XSR)","v":0},{"$f":"IF(AO11<>XSR,AP11+TAN(AP14)*(AO15-AO11),YSR)","v":-1.6687410892032144},{"$f":"IF(AQ11<>XSR,0,XSR)","v":0},{"$f":"IF(AQ11<>XSR,AR11+TAN(AR14)*(AQ15-AQ11),YSR)","v":-5.0068836025717776},{"$f":"IF(AS11<>XSR,0,XSR)","v":0},{"$f":"IF(AS11<>XSR,AT11+TAN(AT14)*(AS15-AS11),YSR)","v":-8.3439293213497905},{"$f":"IF(AU11<>XSR,0,XSR)","v":0},{"$f":"IF(AU11<>XSR,AV11+TAN(AV14)*(AU15-AU11),YSR)","v":-11.677077993886005},{"$f":"IF(AW11<>XSR,0,XSR)","v":0},{"$f":"IF(AW11<>XSR,AX11+TAN(AX14)*(AW15-AW11),YSR)","v":-15.002975443315284},{"$f":"IF(AY11<>XSR,0,XSR)","v":0},{"$f":"IF(AY11<>XSR,AZ11+TAN(AZ14)*(AY15-AY11),YSR)","v":-18.317624639447843},{"$f":"IF(BA11<>XSR,0,XSR)","v":0},{"$f":"IF(BA11<>XSR,BB11+TAN(BB14)*(BA15-BA11),YSR)","v":-21.616283012346997},{"$f":"IF(BC11<>XSR,0,XSR)","v":0},{"$f":"IF(BC11<>XSR,BD11+TAN(BD14)*(BC15-BC11),YSR)","v":-24.89335624312567},"angle of radius","f22",{"$f":"IF(BG10<>0,ASIN(BH10*BG10/ABS(BG10)/RADIUS_OF_SEMICIRCLE),ASIN(BH10/RADIUS_OF_SEMICIRCLE))","v":0.20148234507969404},{"$f":"DEGREES(BG15)","v":11.544088019464917},{"$f":"IF(BI10<>0,ASIN(BJ10*BI10/ABS(BI10)/RADIUS_OF_SEMICIRCLE),ASIN(BJ10/RADIUS_OF_SEMICIRCLE))","v":0.17432051209448263},{"$f":"DEGREES(BI15)","v":9.9878296255730774},{"$f":"IF(BK10<>0,ASIN(BL10*BK10/ABS(BK10)/RADIUS_OF_SEMICIRCLE),ASIN(BL10/RADIUS_OF_SEMICIRCLE))","v":0.14728802775453756},{"$f":"DEGREES(BK15)","v":8.4389823631407328},{"$f":"IF(BM10<>0,ASIN(BN10*BM10/ABS(BM10)/RADIUS_OF_SEMICIRCLE),ASIN(BN10/RADIUS_OF_SEMICIRCLE))","v":0.12036356044196994},{"$f":"DEGREES(BM15)","v":6.896324020492667},{"$f":"IF(BO10<>0,ASIN(BP10*BO10/ABS(BO10)/RADIUS_OF_SEMICIRCLE),ASIN(BP10/RADIUS_OF_SEMICIRCLE))","v":9.3526513837172101E-2},{"$f":"DEGREES(BO15)","v":5.358674515441856},{"$f":"IF(BQ10<>0,ASIN(BR10*BQ10/ABS(BQ10)/RADIUS_OF_SEMICIRCLE),ASIN(BR10/RADIUS_OF_SEMICIRCLE))","v":6.6756875357225187E-2},{"$f":"DEGREES(BQ15)","v":3.8248872114498931},{"$f":"IF(BS10<>0,ASIN(BT10*BS10/ABS(BS10)/RADIUS_OF_SEMICIRCLE),ASIN(BT10/RADIUS_OF_SEMICIRCLE))","v":4.0035075666717559E-2},{"$f":"DEGREES(BS15)","v":2.2938408681898164},{"$f":"IF(BU10<>0,ASIN(BV10*BU10/ABS(BU10)/RADIUS_OF_SEMICIRCLE),ASIN(BV10/RADIUS_OF_SEMICIRCLE))","v":1.33418564069474E-2},{"$f":"DEGREES(BU15)","v":0.76443206298766297},{"$f":"IF(BW10<>0,ASIN(BX10*BW10/ABS(BW10)/RADIUS_OF_SEMICIRCLE),ASIN(BX10/RADIUS_OF_SEMICIRCLE))","v":-1.33418564069474E-2},{"$f":"DEGREES(BW15)","v":-0.76443206298766297},{"$f":"IF(BY10<>0,ASIN(BZ10*BY10/ABS(BY10)/RADIUS_OF_SEMICIRCLE),ASIN(BZ10/RADIUS_OF_SEMICIRCLE))","v":-4.0035075666717553E-2},{"$f":"DEGREES(BY15)","v":-2.2938408681898164},{"$f":"IF(CA10<>0,ASIN(CB10*CA10/ABS(CA10)/RADIUS_OF_SEMICIRCLE),ASIN(CB10/RADIUS_OF_SEMICIRCLE))","v":-6.6756875357225215E-2},{"$f":"DEGREES(CA15)","v":-3.8248872114498949},{"$f":"IF(CC10<>0,ASIN(CD10*CC10/ABS(CC10)/RADIUS_OF_SEMICIRCLE),ASIN(CD10/RADIUS_OF_SEMICIRCLE))","v":-9.3526513837172087E-2},{"$f":"DEGREES(CC15)","v":-5.3586745154418551},{"$f":"IF(CE10<>0,ASIN(CF10*CE10/ABS(CE10)/RADIUS_OF_SEMICIRCLE),ASIN(CF10/RADIUS_OF_SEMICIRCLE))","v":-0.12036356044196993},{"$f":"DEGREES(CE15)","v":-6.8963240204926661},{"$f":"IF(CG10<>0,ASIN(CH10*CG10/ABS(CG10)/RADIUS_OF_SEMICIRCLE),ASIN(CH10/RADIUS_OF_SEMICIRCLE))","v":-0.14728802775453756},{"$f":"DEGREES(CG15)","v":-8.4389823631407328},{"$f":"IF(CI10<>0,ASIN(CJ10*CI10/ABS(CI10)/RADIUS_OF_SEMICIRCLE),ASIN(CJ10/RADIUS_OF_SEMICIRCLE))","v":-0.17432051209448263},{"$f":"DEGREES(CI15)","v":-9.9878296255730774},{"$f":"IF(CK10<>0,ASIN(CL10*CK10/ABS(CK10)/RADIUS_OF_SEMICIRCLE),ASIN(CL10/RADIUS_OF_SEMICIRCLE))","v":-0.20148234507969401},{"$f":"DEGREES(CK15)","v":-11.544088019464915},"f22"]
["x_SO1",{"$f":"X_SOURCE-XC","v":204},null,null,"Angle of tangent from source to circle",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"point at",{"$f":"DEGREES(U15)","v":5.8307833208179112},{"$f":"DEGREES(V15)","v":5.8307833208179112},null,null,"SIN(KLISI)*NN",{"$f":"SIN(Z14)*nn","v":0.2357217068592187},0.2357217068592187,0.23294323170647543,0.23294323170647543,0.23213076693920343,0.23213076693920343,0.23279814140833269,0.23279814140833269,0.23454430749696836,0.23454430749696836,0.2370250522875321,0.2370250522875321,null,0.23993253916084623,0.23993253916084623,0.24297936414933791,0.24297936414933791,0.24588494470291097,0.24588494470291097,0.24836259243332828,0.24836259243332828,0.25010576716126243,0.25010576716126243,0.25077182137482201,0.25077182137482201,0.24996095094317666,0.24996095094317666,0.24718683172921158,0.24718683172921158,0.24183298690117561,0.24183298690117561,"circle left","insi klisi",{"$f":"IF(BG10<>0,PI()+BG14+BG15,BG14)","v":2.3268430743283157E-2},{"$f":"BG16","v":2.3268430743283157E-2},{"$f":"IF(BI10<>0,PI()+BI14+BI15,BI14)","v":2.3268430743283157E-2},{"$f":"BI16","v":2.3268430743283157E-2},{"$f":"IF(BK10<>0,PI()+BK14+BK15,BK14)","v":2.3268430743283157E-2},{"$f":"BK16","v":2.3268430743283157E-2},{"$f":"IF(BM10<>0,PI()+BM14+BM15,BM14)","v":2.3268430743283157E-2},{"$f":"BM16","v":2.3268430743283157E-2},{"$f":"IF(BO10<>0,PI()+BO14+BO15,BO14)","v":2.3268430743283157E-2},{"$f":"BO16","v":2.3268430743283157E-2},{"$f":"IF(BQ10<>0,PI()+BQ14+BQ15,BQ14)","v":2.3268430743283157E-2},{"$f":"BQ16","v":2.3268430743283157E-2},{"$f":"IF(BS10<>0,PI()+BS14+BS15,BS14)","v":2.3268430743283157E-2},{"$f":"BS16","v":2.3268430743283157E-2},{"$f":"IF(BU10<>0,PI()+BU14+BU15,BU14)","v":2.3268430743283157E-2},{"$f":"BU16","v":2.3268430743283157E-2},{"$f":"IF(BW10<>0,PI()+BW14+BW15,BW14)","v":2.3268430743283157E-2},{"$f":"BW16","v":2.3268430743283157E-2},2.3268430743283157E-2,{"$f":"BY16","v":2.3268430743283157E-2},2.3268430743283157E-2,{"$f":"CA16","v":2.3268430743283157E-2},2.3268430743283157E-2,{"$f":"CC16","v":2.3268430743283157E-2},2.3268430743283157E-2,{"$f":"CE16","v":2.3268430743283157E-2},2.3268430743283157E-2,{"$f":"CG16","v":2.3268430743283157E-2},2.3268430743283157E-2,{"$f":"CI16","v":2.3268430743283157E-2},2.3268430743283157E-2,{"$f":"CK16","v":2.3268430743283157E-2},"insi klisi"]
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["if y11>radius we have two angle",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(SIN(U24)*nn<1,-200,U22+RADIUS_OF_SEMICIRCLE*COS(U25))","v":-200},{"$f":"IF(SIN(V24)*nn<1,V22+(-200-U22)*TAN(U26),U22-RADIUS_OF_SEMICIRCLE*SIN(#REF!))","v":-20.179450675576916},null,null,"KLISI_F",{"$f":"-(A_GONIA-DGON*Z33-OMEGA)","v":5.5280820979338174E-3},{"$f":"Z27","v":5.5280820979338174E-3},{"$f":"-(A_GONIA-DGON*AB33-OMEGA)","v":2.9550549489213013E-2},{"$f":"AB27","v":2.9550549489213013E-2},{"$f":"-(A_GONIA-DGON*AD33-OMEGA)","v":5.3573016880492222E-2},{"$f":"AD27","v":5.3573016880492222E-2},{"$f":"-(A_GONIA-DGON*AF33-OMEGA)","v":7.7595484271771417E-2},{"$f":"AF27","v":7.7595484271771417E-2},{"$f":"-(A_GONIA-DGON*AH33-OMEGA)","v":0.10161795166305061},{"$f":"AH27","v":0.10161795166305061},{"$f":"-(A_GONIA-DGON*AJ33-OMEGA)","v":0.12564041905432982},{"$f":"AJ27","v":0.12564041905432982},null,{"$f":"-(A_GONIA-DGON*AM33-OMEGA)","v":0.14966288644560902},{"$f":"AM27","v":0.14966288644560902},{"$f":"-(A_GONIA-DGON*AO33-OMEGA)","v":0.17368535383688821},{"$f":"AO27","v":0.17368535383688821},{"$f":"-(A_GONIA-DGON*AQ33-OMEGA)","v":0.19770782122816741},{"$f":"AQ27","v":0.19770782122816741},{"$f":"-(A_GONIA-DGON*AS33-OMEGA)","v":0.2217302886194466},{"$f":"AS27","v":0.2217302886194466},{"$f":"-(A_GONIA-DGON*AU33-OMEGA)","v":0.2457527560107258},{"$f":"AU27","v":0.2457527560107258},{"$f":"-(A_GONIA-DGON*AW33-OMEGA)","v":0.26977522340200499},{"$f":"AW27","v":0.26977522340200499},{"$f":"-(A_GONIA-DGON*AY33-OMEGA)","v":0.29379769079328422},{"$f":"AY27","v":0.29379769079328422},{"$f":"-(A_GONIA-DGON*BA33-OMEGA)","v":0.31782015818456344},{"$f":"BA27","v":0.31782015818456344},{"$f":"-(A_GONIA-DGON*BC33-OMEGA)","v":0.34184262557584255},{"$f":"BC27","v":0.34184262557584255},"SINE OF ANGLE","refraction",{"$f":"SIN(BG22)*nn","v":0.30010160447270989},{"$f":"(BG21*(BH21-BH10)-BH21*(BG21-BG10))/RADIUS_OF_SEMICIRCLE/SQRT((BG21-BG10)^2+(BH21-BH10)^2)","v":0.20006773631513994},{"$f":"SIN(BI22)*nn","v":0.26008805720968192},{"$f":"(BI21*(BJ21-BJ10)-BJ21*(BI21-BI10))/RADIUS_OF_SEMICIRCLE/SQRT((BI21-BI10)^2+(BJ21-BJ10)^2)","v":0.17339203813978796},{"$f":"SIN(BK22)*nn","v":0.22007450994665392},{"$f":"(BK21*(BL21-BL10)-BL21*(BK21-BK10))/RADIUS_OF_SEMICIRCLE/SQRT((BK21-BK10)^2+(BL21-BL10)^2)","v":0.14671633996443595},{"$f":"SIN(BM22)*nn","v":0.18006096268362592},{"$f":"(BM21*(BN21-BN10)-BN21*(BM21-BM10))/RADIUS_OF_SEMICIRCLE/SQRT((BM21-BM10)^2+(BN21-BN10)^2)","v":0.12004064178908394},{"$f":"SIN(BO22)*nn","v":0.14004741542059798},{"$f":"(BO21*(BP21-BP10)-BP21*(BO21-BO10))/RADIUS_OF_SEMICIRCLE/SQRT((BO21-BO10)^2+(BP21-BP10)^2)","v":9.3364943613731988E-2},{"$f":"SIN(BQ22)*nn","v":0.10003386815756989},{"$f":"(BQ21*(BR21-BR10)-BR21*(BQ21-BQ10))/RADIUS_OF_SEMICIRCLE/SQRT((BQ21-BQ10)^2+(BR21-BR10)^2)","v":6.6689245438379938E-2},{"$f":"SIN(BS22)*nn","v":6.0020320894541977E-2},{"$f":"(BS21*(BT21-BT10)-BT21*(BS21-BS10))/RADIUS_OF_SEMICIRCLE/SQRT((BS21-BS10)^2+(BT21-BT10)^2)","v":4.0013547263027985E-2},{"$f":"SIN(BU22)*nn","v":2.0006773631513992E-2},{"$f":"(BU21*(BV21-BV10)-BV21*(BU21-BU10))/RADIUS_OF_SEMICIRCLE/SQRT((BU21-BU10)^2+(BV21-BV10)^2)","v":1.3337849087675996E-2},{"$f":"SIN(BW22)*nn","v":-2.0006773631513992E-2},{"$f":"(BW21*(BX21-BX10)-BX21*(BW21-BW10))/RADIUS_OF_SEMICIRCLE/SQRT((BW21-BW10)^2+(BX21-BX10)^2)","v":-1.3337849087675994E-2},{"$f":"SIN(BY22)*nn","v":-6.0020320894541977E-2},{"$f":"(BY21*(BZ21-BZ10)-BZ21*(BY21-BY10))/RADIUS_OF_SEMICIRCLE/SQRT((BY21-BY10)^2+(BZ21-BZ10)^2)","v":-4.0013547263027985E-2},{"$f":"SIN(CA22)*nn","v":-0.10003386815756997},{"$f":"(CA21*(CB21-CB10)-CB21*(CA21-CA10))/RADIUS_OF_SEMICIRCLE/SQRT((CA21-CA10)^2+(CB21-CB10)^2)","v":-6.6689245438379979E-2},{"$f":"SIN(CC22)*nn","v":-0.14004741542059793},{"$f":"(CC21*(CD21-CD10)-CD21*(CC21-CC10))/RADIUS_OF_SEMICIRCLE/SQRT((CC21-CC10)^2+(CD21-CD10)^2)","v":-9.3364943613731946E-2},{"$f":"SIN(CE22)*nn","v":-0.18006096268362595},{"$f":"(CE21*(CF21-CF10)-CF21*(CE21-CE10))/RADIUS_OF_SEMICIRCLE/SQRT((CE21-CE10)^2+(CF21-CF10)^2)","v":-0.12004064178908395},{"$f":"SIN(CG22)*nn","v":-0.22007450994665392},{"$f":"(CG21*(CH21-CH10)-CH21*(CG21-CG10))/RADIUS_OF_SEMICIRCLE/SQRT((CG21-CG10)^2+(CH21-CH10)^2)","v":-0.14671633996443595},{"$f":"SIN(CI22)*nn","v":-0.26008805720968192},{"$f":"(CI21*(CJ21-CJ10)-CJ21*(CI21-CI10))/RADIUS_OF_SEMICIRCLE/SQRT((CI21-CI10)^2+(CJ21-CJ10)^2)","v":-0.17339203813978796},{"$f":"SIN(CK22)*nn","v":-0.30010160447270984},{"$f":"(CK21*(CL21-CL10)-CL21*(CK21-CK10))/RADIUS_OF_SEMICIRCLE/SQRT((CK21-CK10)^2+(CL21-CL10)^2)","v":-0.20006773631513991},"refraction","incidence"]
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[]
[]
[]
[]
["h",{"$f":"h","v":1.8},{"$f":"(h-YC)*SIN(radiansg)","v":6.2819094064501743E-2},{"$f":"radiansg","v":3.4906585039886591E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AK129","v":1.2430711841385302},{"$f":"(-TAN(critical_angle)*AC127+SQRT(RADIUS_OF_SEMICIRCLE^2*(TAN(critical_angle)^2+1)-AC127^2))/(TAN(critical_angle)^2+1)","v":55.279746520833299},{"$f":"AC127+TAN(critical_angle)*AD127","v":50.686779583954831},{"$f":"ATAN(AE127/AD127)","v":0.74208171122541011},{"$f":"ATAN((AE127-htry)/(AD127-htrx))","v":0.72355003941976426},{"$f":"(AF127-critical_angle)","v":1.2354054998443775E-2},{"$f":"IF(ABS(SIN(AH127)*nn)<1,ASIN(SIN(AH127)*nn),-3)","v":1.8531671805774658E-2},{"$f":"AF127-AG127","v":1.8531671805645855E-2},{"$f":"IF(OR(AL127,AI127>AJ127),1,0)","v":1},null,{"$f":"1","v":1},{"$f":"TAN(AG127)","v":0.88336844438162809},{"$f":"((htrx*AN127-htry)*AN127+SQRT(rad_of_gon^2*(AN127^2+1)-(htrx*AN127-htry)^2))/(AN127^2+1)","v":111.49408423103117},{"$f":"htry+AN127*(AO127-htrx)","v":100.34475163895581},{"$f":"DEGREES(AN127)","v":50.61328361810429}]
[null,"htrx","htry","the point at which the ray meets the y axis in the transformed ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"T1","T2","find yd1"]
[null,{"$f":"(0-XC)*COS(radiansg)-(h-YC)*SIN(radiansg)","v":-6.2819094064501743E-2},{"$f":"(0-XC)*SIN(radiansg)+(h-YC)*COS(radiansg)","v":1.7989034886343724},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AI131/AC131","v":1.4909325986994851E-2},{"$f":"AJ131/AC131","v":-1.5378469921355141E-4},{"$f":"(AJ138-AI138)/(AI129-AJ129)+AC138","v":1.2430711841385302},{"$f":"(AJ132-AI132)/(AI129-AJ129)","v":0}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"single ray",null,null,null,null,null,null,null,{"$f":"AC133-AC138","v":0.18057094061455126},{"$f":"AD133-AD138","v":-9.0875778945886054E-2},9.9289172922048863E-2,1.7946464546179097E-3,1.8224155024070265E-3,1.7946464546179097E-3,{"$f":"AI133-AI138","v":2.692191017400633E-3},-2.7769047789116819E-5,{"$f":"AK141-AK133","v":0}]
[null,6,6,10,{"$f":"D132","v":10},{"$f":"D132+10","v":20},{"$f":"F132","v":20},{"$f":"F132+10","v":30},{"$f":"H132","v":30},{"$f":"H132+10","v":40},{"$f":"J132","v":40},{"$f":"J132+10","v":50},{"$f":"L132","v":50},{"$f":"L132+10","v":60},{"$f":"N132","v":60},{"$f":"N132+10","v":70},{"$f":"P132","v":70},{"$f":"P132+10","v":80},{"$f":"R132","v":80},null,{"$f":"THETA","v":34},{"$f":"U132","v":34}]
[null,{"$f":"RADIANS(B132)","v":0.10471975511965978},0.10471975511965978,0.17453292519943295,0.17453292519943295,0.3490658503988659,0.3490658503988659,0.52359877559829882,0.52359877559829882,0.69813170079773179,0.69813170079773179,0.87266462599716477,0.87266462599716477,1.0471975511965976,1.0471975511965976,1.2217304763960306,1.2217304763960306,1.3962634015954636,1.3962634015954636,null,{"$f":"Semicircle!A57/10","v":34},{"$f":"RADIANS(U133)","v":0.59341194567807209},null,null,null,null,null,null,{"$f":"AM136","v":1.2430709406145513},{"$f":"(-TAN(critical_angle)*AC133+SQRT(RADIUS_OF_SEMICIRCLE^2*(TAN(critical_angle)^2+1)-AC133^2))/(TAN(critical_angle)^2+1)","v":55.279746643512802},{"$f":"AC133+TAN(critical_angle)*AD133","v":50.686779450158731},{"$f":"ATAN(AE133/AD133)","v":0.74208170880506452},{"$f":"ATAN((AE133-htry)/(AD133-htrx))","v":0.72355003696192599},{"$f":"(AF133-critical_angle)","v":1.2354052578098185E-2},{"$f":"IF(ABS(SIN(AH133)*nn)<1,ASIN(SIN(AH133)*nn),-3)","v":1.8531668174909879E-2},{"$f":"AF133-AG133","v":1.8531671843138531E-2},{"$f":"IF(OR(AL133,AI133>AJ133),1,0)","v":0},null,{"$f":"1","v":1},{"$f":"TAN(AG133)","v":0.8833684400058408},{"$f":"((htrx*AN133-htry)*AN133+SQRT(rad_of_gon^2*(AN133^2+1)-(htrx*AN133-htry)^2))/(AN133^2+1)","v":111.49408447578148},{"$f":"htry+AN133*(AO133-htrx)","v":100.34475136701123},{"$f":"DEGREES(AN133)","v":50.613283367390146}]
["X1,Y1",{"$f":"150*COS(B133)","v":149.17828430524099},{"$f":"150*SIN(C133)","v":15.679269490148021},{"$f":"150*COS(D133)","v":147.72116295183119},{"$f":"150*SIN(E133)","v":26.047226650039551},{"$f":"150*COS(F133)","v":140.95389311788625},{"$f":"150*SIN(G133)","v":51.303021498850306},{"$f":"150*COS(H133)","v":129.9038105676658},{"$f":"150*SIN(I133)","v":74.999999999999986},{"$f":"150*COS(J133)","v":114.9066664678467},{"$f":"150*SIN(K133)","v":96.41814145298089},{"$f":"150*COS(L133)","v":96.418141452980905},{"$f":"150*SIN(M133)","v":114.9066664678467},{"$f":"150*COS(N133)","v":75.000000000000014},{"$f":"150*SIN(O133)","v":129.9038105676658},{"$f":"150*COS(P133)","v":51.30302149885032},{"$f":"150*SIN(Q133)","v":140.95389311788625},{"$f":"150*COS(R133)","v":26.047226650039562},{"$f":"150*SIN(S133)","v":147.72116295183119},"X1,Y1",{"$f":"150*COS(V133)","v":124.35563588325624},{"$f":"150*SIN(V133)","v":83.878935520612032},"X1,Y1",null,null,null,null,null,null,null,null,null,null,null,"T1","T2","find yd1",null,null,null,null,"INC1=INC10+T1*(yd1-yd10)"]
[null,"we do a transformation by xc, yc ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AI137/AC137","v":1.4909339595731911E-2},{"$f":"AJ137/AC137","v":-1.5379140508879155E-4},{"$f":"(AJ138-AI138)/(AI135-AJ135)+AC138","v":1.2430709406145513},{"$f":"(AJ138-AI138)/(AI135-AJ135)","v":0.18057094061455128},null,null,null,"INC2=INC20+T2(yd1-yd10)"]
[null,{"$f":"B134-XC","v":149.17828430524099},{"$f":"C134-YC","v":15.679269490148021},{"$f":"D134-XC","v":147.72116295183119},{"$f":"E134-YC","v":26.047226650039551},{"$f":"F134-XC","v":140.95389311788625},{"$f":"G134-YC","v":51.303021498850306},{"$f":"H134-XC","v":129.9038105676658},{"$f":"I134-YC","v":74.999999999999986},{"$f":"J134-XC","v":114.9066664678467},{"$f":"K134-YC","v":96.41814145298089},{"$f":"L134-XC","v":96.418141452980905},{"$f":"M134-YC","v":114.9066664678467},{"$f":"N134-XC","v":75.000000000000014},{"$f":"O134-YC","v":129.9038105676658},{"$f":"P134-XC","v":51.30302149885032},{"$f":"Q134-YC","v":140.95389311788625},{"$f":"R134-XC","v":26.047226650039562},{"$f":"S134-YC","v":147.72116295183119},null,{"$f":"U134-XC","v":124.35563588325624},{"$f":"V134-YC","v":83.878935520612032},null,null,null,null,null,null,null,null,null,"DTHETA2","DTHETA1","DREFR","DINC1","DINC2","dy",null,{"$f":"AK135","v":1.2430709406145513},null,null,"yd1*(T1-T2)=INC20-INC10+yd10*(T1-T2)"]
["IN ROTATED","we do a transformation by gonia",null,null,null,"x11=x1cosg-y1singy11=x1sing+y1cosg",null,null,null,null,null,null,null,null,null,null,null,null,null,"IN ROTATED",null,null,"IN ROTATED",null,null,null,null,null,{"$f":"-AC138+AC141","v":0.1875},{"$f":"-AD138+AD141","v":-9.4366547873242723E-2},{"$f":"-AE138+AE141","v":0.10309599366137689},{"$f":"-AF138+AF141","v":1.8635132850225444E-3},{"$f":"-AG138+AG141","v":1.8923491734766928E-3},1.8635132850225444E-3,{"$f":"-AI138+AI141","v":2.7955011741997333E-3},-2.8835888454148417E-5,null,null,{"$f":"DEGREES(AM136)","v":71.222718532571179},null,null,"yd1=(INC20-INC10)/(T1-T2)+yd10"]
["X1,Y1",{"$f":"B136*COS(radiansg)-C136*SIN(radiansg)","v":148.54021031123554},{"$f":"B136*SIN(radiansg)+C136*COS(radiansg)","v":20.875965144009818},{"$f":"D136*COS(radiansg)-E136*SIN(radiansg)","v":146.72214011007082},{"$f":"D136*SIN(radiansg)+E136*COS(radiansg)","v":31.1867536226639},{"$f":"F136*COS(radiansg)-G136*SIN(radiansg)","v":139.07757818501813},{"$f":"F136*SIN(radiansg)+G136*COS(radiansg)","v":56.190989012386801},{"$f":"H136*COS(radiansg)-I136*SIN(radiansg)","v":127.20721442346391},{"$f":"H136*SIN(radiansg)+I136*COS(radiansg)","v":79.487889634980732},{"$f":"J136*COS(radiansg)-K136*SIN(radiansg)","v":111.47172382160915},{"$f":"J136*SIN(radiansg)+K136*COS(radiansg)","v":100.36959095382872},{"$f":"L136*COS(radiansg)-M136*SIN(radiansg)","v":92.349221298848747},{"$f":"L136*SIN(radiansg)+M136*COS(radiansg)","v":118.2016130410083},{"$f":"N136*COS(radiansg)-O136*SIN(radiansg)","v":70.420734417883622},{"$f":"N136*SIN(radiansg)+O136*COS(radiansg)","v":132.44213892883906},{"$f":"P136*COS(radiansg)-Q136*SIN(radiansg)","v":46.352549156242127},{"$f":"P136*SIN(radiansg)+Q136*COS(radiansg)","v":142.65847744427305},{"$f":"R136*COS(radiansg)-S136*SIN(radiansg)","v":20.875965144009829},{"$f":"R136*SIN(radiansg)+S136*COS(radiansg)","v":148.54021031123551},"X1,Y1",{"$f":"U136*COS(radiansg)-V136*SIN(radiansg)","v":121.35254915624211},{"$f":"U136*SIN(radiansg)+V136*COS(radiansg)","v":88.167787843870983},"X1,Y1",0,{"$f":"150","v":150},null,null,null,{"$f":"AC141-RADIUS_OF_SEMICIRCLE/400","v":1.0625},{"$f":"(-TAN(critical_angle)*AC138+SQRT(RADIUS_OF_SEMICIRCLE^2*(TAN(critical_angle)^2+1)-AC138^2))/(TAN(critical_angle)^2+1)","v":55.370622422458688},{"$f":"AC138+TAN(critical_angle)*AD138","v":50.587490277236682},{"$f":"ATAN(AE138/AD138)","v":0.74028706235044661},{"$f":"ATAN((AE138-htry)/(AD138-htrx))","v":0.72172762145951896},{"$f":"(AF138-critical_angle)","v":1.0559406123480275E-2},{"$f":"IF(ABS(SIN(AH138)*nn)<1,ASIN(SIN(AH138)*nn),-3)","v":1.5839477157509246E-2},{"$f":"AF138-AG138","v":1.8559440890927648E-2},{"$f":"IF(OR(AL138,AI138>AJ138),1,0)","v":0},null,{"$f":"1","v":1},{"$f":"TAN(AG138)","v":0.88012913241296342},{"$f":"((htrx*AN138-htry)*AN138+SQRT(rad_of_gon^2*(AN138^2+1)-(htrx*AN138-htry)^2))/(AN138^2+1)","v":111.67537881107093},{"$f":"htry+AN138*(AO138-htrx)","v":100.14294666826922},{"$f":"DEGREES(AN138)","v":50.427684713773587}]
[null,"we find the point at which the line from x1, y1 meets the radius",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"DEGREES(AF138)","v":42.415324300818618}]
[null,"the point y at whih it cuts the diameter is (0,h) in lab so it is (-xc, h-yc) in the fist trnsforamtion and it is (htrx, htry) by the second transformation",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"y","x2","y2","θ2","θ1","refraction","inc","INC 2"]
["X=0,Y=h",{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},"X=0,Y=h",{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},"X=0,Y=h",null,null,null,null,null,{"$f":"VLOOKUP(1,AB146:AK546,2,FALSE)","v":1.25},{"$f":"VLOOKUP(1,AB146:AL546,3,FALSE)","v":55.276255874585445},{"$f":"VLOOKUP(1,AB146:AK546,4,FALSE)","v":50.690586270898059},{"$f":"VLOOKUP(1,AB146:AK546,5,FALSE)","v":0.74215057563546916},{"$f":"VLOOKUP(1,AB146:AK546,6,FALSE)","v":0.72361997063299566},{"$f":"VLOOKUP(1,AB146:AK546,7,FALSE)","v":1.2422919408502819E-2},{"$f":"VLOOKUP(1,AB146:AK546,8,FALSE)","v":1.863497833170898E-2},{"$f":"VLOOKUP(1,AB146:AM546,9,FALSE)","v":1.8530605002473499E-2},null,null,{"$f":"VLOOKUP(1,AB146:AM546,11,FALSE)","v":0},{"$f":"VLOOKUP(1,AB146:AP546,13,FALSE)","v":0.88349295339615341},{"$f":"VLOOKUP(1,AB146:AP546,14,FALSE)","v":111.48712024948863},null,null,null,"we find the x1 in transformed plane by finding the cut from htrx,htry to the circle of radius 150"]
[null,"we calculate the refraction angle in the new frame sin(theta) = sin(incidence)/n",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1","v":1},{"$f":"AB142+1","v":2},{"$f":"AC142+1","v":3},4,5,6,7,8,9,10,null,{"$f":"AK142+1","v":11},null,null,null,null,null,null,"tthet1"]
["incidence",{"$f":"ATAN((C138-htry)/(B138-htrx))","v":0.12767765764707673},{"$f":"B143","v":0.12767765764707673},{"$f":"ATAN((E138-htry)/(D138-htrx))","v":0.19759769388327875},{"$f":"D143","v":0.19759769388327875},{"$f":"ATAN((G138-htry)/(F138-htrx))","v":0.37265013639487443},{"$f":"F143","v":0.37265013639487443},{"$f":"ATAN((I138-htry)/(H138-htrx))","v":0.54805070649626975},{"$f":"H143","v":0.54805070649626975},{"$f":"ATAN((K138-htry)/(J138-htrx))","v":0.7237745601822031},{"$f":"J143","v":0.7237745601822031},{"$f":"ATAN((M138-htry)/(L138-htrx))","v":0.8997863529763882},{"$f":"L143","v":0.8997863529763882},{"$f":"ATAN((O138-htry)/(N138-htrx))","v":1.0760412018930554},{"$f":"N143","v":1.0760412018930554},{"$f":"ATAN((Q138-htry)/(P138-htrx))","v":1.2524860350227911},{"$f":"P143","v":1.2524860350227911},{"$f":"ATAN((S138-htry)/(R138-htrx))","v":1.4290612916822574},{"$f":"R143","v":1.4290612916822574},"incidence",{"$f":"ATAN((V138-htry)/(U138-htrx))","v":0.61830320650295456},{"$f":"U143","v":0.61830320650295456},"incidence",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x1",{"$f":"AO127","v":111.49408423103117},"y1",{"$f":"AP127","v":100.34475163895581}]
["in degrees",{"$f":"DEGREES(B143)","v":7.3153909212937176},{"$f":"DEGREES(C143)","v":7.3153909212937176},{"$f":"DEGREES(D143)","v":11.321513901029874},11.321513901029874,21.351280050400781,21.351280050400781,31.400992441399264,31.400992441399264,41.469227617377641,41.469227617377641,51.553960489015601,51.553960489015601,{"$f":"DEGREES(N143)","v":61.652619450656601},61.652619450656601,71.762163705880539,71.762163705880539,81.879180678907247,81.879180678907247,"in degrees",{"$f":"DEGREES(U143)","v":35.426164192025091},{"$f":"DEGREES(V143)","v":35.426164192025091},"in degrees",null,null,null,"at circle",{"$f":"SUM(AB146:AB302)","v":0},{"$f":"COUNTA(AC146:AC302)","v":157},null,null,"for point on circle","for line from htrx, htry to point on circle","refraction angle in the case the refracted is the critical angle","incident angle in case refracted= critical","incident angle  = θ2-θ1","comparison of the two angles (8 and 9)",null,null,"rad of gon",150]
["refraction",{"$f":"ASIN(SIN(B143)/nn)","v":8.498964577480965E-2},8.498964577480965E-2,0.13125275689655763,0.13125275689655763,0.24517212137742589,0.24517212137742589,0.35474324776981198,0.35474324776981198,0.45724574520426392,0.45724574520426392,0.54934579473390777,0.54934579473390777,0.62700655727549348,0.62700655727549348,0.68565104489438033,0.68565104489438033,0.72079426352504528,0.72079426352504528,"refraction",{"$f":"ASIN(SIN(U143)/nn)","v":0.39676378915061622},{"$f":"ASIN(SIN(V143)/nn)","v":0.39676378915061622},"refraction",null,null,null,null,null,"ytrial","x2","y2","θ2","θ1","ref","inc",null,null,null,null,"TTHET1","X1","Y1"]
["in degrees",{"$f":"DEGREES(B145)","v":4.8695480052084621},{"$f":"DEGREES(C145)","v":4.8695480052084621},7.5202290196293617,7.5202290196293617,14.04732780919565,14.04732780919565,20.32529090797388,20.32529090797388,26.198251400518526,26.198251400518526,31.475195531512959,31.475195531512959,{"$f":"DEGREES(N145)","v":35.9248294589135},35.9248294589135,39.284911091182927,39.284911091182927,41.29846919722555,41.29846919722555,"in degrees",{"$f":"DEGREES(U145)","v":22.732890581948791},{"$f":"DEGREES(V145)","v":22.732890581948791},"in degrees",null,null,null,null,{"$f":"IF(ISERROR(AK146),0,IF(AK146=1,1+AB145,0))","v":0},{"$f":"-RADIUS_OF_SEMICIRCLE","v":-75},{"$f":"(-TAN(critical_angle)*AC146+SQRT(RADIUS_OF_SEMICIRCLE^2*(TAN(critical_angle)^2+1)-AC146^2))/(TAN(critical_angle)^2+1)","v":74.535599249992984},{"$f":"AC146+TAN(critical_angle)*AD146","v":-8.3333333333333428},{"$f":"ATAN(AE146/AD146)","v":-0.11134101434096402},{"$f":"ATAN((AE146-htry)/(AD146-htrx))","v":-0.13499764396029984},{"$f":"(AF146-critical_angle)","v":-0.84106867056793033},{"$f":"IF(ABS(SIN(AH146)*nn)<1,ASIN(SIN(AH146)*nn),-3)","v":-3},{"$f":"AF146-AG146","v":2.3656629619335817E-2},{"$f":"IF(OR(AL146,AI146>AJ146),1,0)","v":0},null,{"$f":"1","v":1},{"$f":"TAN(AG146)","v":-0.13582374863816196},{"$f":"((htrx*AN146-htry)*AN146+SQRT(rad_of_gon^2*(AN146^2+1)-(htrx*AN146-htry)^2))/(AN146^2+1)","v":148.86362118548374},{"$f":"htry+AN146*(AO146-htrx)","v":-18.428843901471225},{"$f":"DEGREES(AN146)","v":-7.7821275546124431}]
["X2,Y2",{"$f":"0","v":0},{"$f":"C138+(0-B138)*TAN(C143)","v":1.8069679522957074},{"$f":"0","v":0},{"$f":"E138+(0-D138)*TAN(E143)","v":1.8114805137732795},{"$f":"0","v":0},{"$f":"G138+(0-F138)*TAN(G143)","v":1.8234604225205686},{"$f":"0","v":0},{"$f":"I138+(0-H138)*TAN(I143)","v":1.8372499209689863},{"$f":"0","v":0},{"$f":"K138+(0-J138)*TAN(K143)","v":1.8544210092697568},{"$f":"0","v":0},{"$f":"M138+(0-L138)*TAN(M143)","v":1.8780307617650607},{"$f":"0","v":0},{"$f":"O138+(0-N138)*TAN(O143)","v":1.9153404343769296},{"$f":"0","v":0},{"$f":"Q138+(0-P138)*TAN(Q143)","v":1.9895444586356916},{"$f":"0","v":0},{"$f":"S138+(0-R138)*TAN(S143)","v":2.239146620787011},"X2,Y2",{"$f":"0","v":0},{"$f":"V138+(0-U138)*TAN(V143)","v":1.8435898833531326},"X2,Y2",0,{"$f":"RADIUS_OF_SEMICIRCLE","v":75},null,null,0,{"$f":"AC146+RADIUS_OF_SEMICIRCLE/300","v":-74.75},74.566075852039845,-8.0560742317733514,{"$f":"ATAN(AE147/AD147)","v":-0.10762195777373033},-0.13129346122710742,-0.83734961400069663,-3,{"$f":"AF147-AG147","v":2.3671503453377082E-2},0,null,{"$f":"AM146+1","v":2},{"$f":"TAN(AG147)","v":-0.13205311062859515},148.93099647926107,-17.876193322246493,{"$f":"DEGREES(AN147)","v":-7.5660859105926557}]
["point at","semicricel we must find the cut of semicircel with the line that has inclination -angle of refraction and starting point htrx, htry with circel (x))^2+(y)^2=R^2",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"point at",null,null,"point at",null,null,null,null,0,-74.5,74.595402190784696,-7.7798439569874773,-0.10391818703298791,-0.12760418158523859,-0.83364584325995428,-3,2.3685994552250678E-2,0,null,{"$f":"AM147+1","v":3},{"$f":"TAN(AG148)","v":-0.12830130802440798},148.99605858368031,-17.325545490070514,-7.3511234558065395]
["semcircele",{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(B145))^2)-(C147-B147*TAN(B145))^2","v":5662.5620520558195},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(C145))^2)-(C147-B147*TAN(C145))^2","v":5662.5620520558195},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(D145))^2)-(E147-D147*TAN(D145))^2","v":5719.7459087433317},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(E145))^2)-(E147-D147*TAN(E145))^2","v":5719.7459087433317},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(F145))^2)-(G147-F147*TAN(F145))^2","v":5973.815865401154},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(G145))^2)-(G147-F147*TAN(G145))^2","v":5973.815865401154},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(H145))^2)-(I147-H147*TAN(H145))^2","v":6393.4076009594728},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(I145))^2)-(I147-H147*TAN(I145))^2","v":6393.4076009594728},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(J145))^2)-(K147-J147*TAN(J145))^2","v":6983.2989554912219},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(K145))^2)-(K147-J147*TAN(K145))^2","v":6983.2989554912219},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(L145))^2)-(M147-L147*TAN(L145))^2","v":7729.6977909677989},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(M145))^2)-(M147-L147*TAN(M145))^2","v":7729.6977909677989},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(N145))^2)-(O147-N147*TAN(N145))^2","v":8574.2207486028547},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(O145))^2)-(O147-N147*TAN(O145))^2","v":8574.2207486028547},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(P145))^2)-(Q147-P147*TAN(P145))^2","v":9385.3320249149565},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(Q145))^2)-(Q147-P147*TAN(Q145))^2","v":9385.3320249149565},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(R145))^2)-(S147-R147*TAN(R145))^2","v":9960.8931962521528},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(S145))^2)-(S147-R147*TAN(S145))^2","v":9960.8931962521528},"semcircele",{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(U145))^2)-(V147-U147*TAN(U145))^2","v":6609.0550674648366},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(V145))^2)-(V147-U147*TAN(V145))^2","v":6609.0550674648366},"semcircele",null,null,null,null,0,-74.25,74.623592310712951,-7.504629947206098,-0.10022946498203812,-0.12392957248977694,-0.82995712120900444,-3,2.3700107507738821E-2,0,null,4,-0.1245679536725653,149.05883548460292,-16.776875870497356,-7.137218008019155]
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["X3,Y3",{"$f":"(-(C147-B147*TAN(B145))-SQRT(B149))/(1+(TAN(B145))^2)","v":-76.501702896798633},{"$f":"C147+TAN(C145)*(B151-B147)","v":-4.7105848558511028},{"$f":"(-(E147-D147*TAN(D145))-SQRT(D149))/(1+(TAN(D145))^2)","v":-76.114036270417301},{"$f":"E147+TAN(E145)*(D151-D147)","v":-8.2364625583044084},{"$f":"(-(G147-F147*TAN(F145))-SQRT(F149))/(1+(TAN(F145))^2)","v":-74.452959327343351},{"$f":"G147+TAN(G145)*(F151-F147)","v":-16.80508391016609},{"$f":"(-(I147-H147*TAN(H145))-SQRT(H149))/(1+(TAN(H145))^2)","v":-71.927201644455266},{"$f":"I147+TAN(I145)*(H151-H147)","v":-24.805529533045981},{"$f":"(-(K147-J147*TAN(J145))-SQRT(J149))/(1+(TAN(J145))^2)","v":-68.771813153203567},{"$f":"K147+TAN(K145)*(J151-J147)","v":-31.982899334030797},{"$f":"(-(M147-L147*TAN(L145))-SQRT(L149))/(1+(TAN(L145))^2)","v":-65.316426667936312},{"$f":"M147+TAN(M145)*(L151-L147)","v":-38.109041901769729},{"$f":"(-(O147-N147*TAN(N145))-SQRT(N149))/(1+(TAN(N145))^2)","v":-61.977066155927574},{"$f":"O147+TAN(O145)*(N151-N147)","v":-42.989518039615689},{"$f":"(-(Q147-P147*TAN(P145))-SQRT(P149))/(1+(TAN(P145))^2)","v":-59.230196076208394},{"$f":"Q147+TAN(Q145)*(P151-P147)","v":-46.463766824348369},{"$f":"(-(S147-R147*TAN(R145))-SQRT(R149))/(1+(TAN(R145))^2)","v":-57.595785809229952},{"$f":"S147+TAN(S145)*(R151-R147)","v":-48.357261152941696},"X3,Y3",{"$f":"(-(V147-U147*TAN(U145))-SQRT(U149))/(1+(TAN(U145))^2)","v":-70.724232690247845},{"$f":"V147+TAN(V145)*(U151-U147)","v":-27.788712290602195},"X3,Y3",null,null,null,null,0,-73.75,74.67661843706064,-6.9572019379673264,-9.2896246183713241E-2,-0.11662346300399629,-0.82262390241067962,-3,2.3727216820283045E-2,0,null,6,-0.1171550886097481,149.17764235913631,-15.685375997075067,-6.7124921258197494]
["ext prod",{"$f":"(B151*(C151-C147)-C151*(B151-B147))","v":138.23612543056282},{"$f":"SQRT((B151-B147)^2+(C151-C147)^2)*RADIUS_OF_SEMICIRCLE","v":5758.4123987461417},{"$f":"(D151*(E151-E147)-E151*(D151-D147))","v":137.87909352849351},{"$f":"SQRT((D151-D147)^2+(E151-E147)^2)*RADIUS_OF_SEMICIRCLE","v":5758.0796004498661},{"$f":"(F151*(G151-G147)-G151*(F151-F147))","v":135.76202467294411},{"$f":"SQRT((F151-F147)^2+(G151-G147)^2)*RADIUS_OF_SEMICIRCLE","v":5756.1050388362246},{"$f":"(H151*(I151-I147)-I151*(H151-H147))","v":132.14824553679591},{"$f":"SQRT((H151-H147)^2+(I151-I147)^2)*RADIUS_OF_SEMICIRCLE","v":5752.7298031530599},{"$f":"(J151*(K151-K147)-K151*(J151-J147))","v":127.53189515687518},{"$f":"SQRT((J151-J147)^2+(K151-K147)^2)*RADIUS_OF_SEMICIRCLE","v":5748.4094969580801},{"$f":"(L151*(M151-M147)-M151*(L151-L147))","v":122.66625853095593},{"$f":"SQRT((L151-L147)^2+(M151-M147)^2)*RADIUS_OF_SEMICIRCLE","v":5743.8453014836023},{"$f":"(N151*(O151-O147)-O151*(N151-N147))","v":118.70718081250243},{"$f":"SQRT((N151-N147)^2+(O151-O147)^2)*RADIUS_OF_SEMICIRCLE","v":5740.1234413332613},{"$f":"(P151*(Q151-Q147)-Q151*(P151-P147))","v":117.84110838732568},{"$f":"SQRT((P151-P147)^2+(Q151-Q147)^2)*RADIUS_OF_SEMICIRCLE","v":5739.3082942114297},{"$f":"(R151*(S151-S147)-S151*(R151-R147))","v":128.96540916630966},{"$f":"SQRT((R151-R147)^2+(S151-S147)^2)*RADIUS_OF_SEMICIRCLE","v":5749.7521252709867},"ext prod",{"$f":"(U151*(V151-V147)-V151*(U151-U147))","v":130.38647989565379},{"$f":"SQRT((U151-U147)^2+(V151-V147)^2)*RADIUS_OF_SEMICIRCLE","v":5751.082169675562},"ext prod",null,null,null,null,0,-73.5,74.701480929014267,-6.6849642491279866,-8.9251302398903831E-2,-0.11299152423474204,-0.81897895862587022,-3,2.374022183583821E-2,0,null,7,-0.11347485009748635,149.23372510715106,-15.142499484671308,-6.5016299914656459]
["sec incidence",{"$f":"ASIN(B152/C152)","v":2.400825028565956E-2},{"$f":"B153","v":2.400825028565956E-2},{"$f":"ASIN(D152/E152)","v":2.3947614943205263E-2},{"$f":"D153","v":2.3947614943205263E-2},{"$f":"ASIN(F152/G152)","v":2.3587932121671151E-2},{"$f":"F153","v":2.3587932121671151E-2},{"$f":"ASIN(H152/I152)","v":2.2973418695161264E-2},{"$f":"H153","v":2.2973418695161264E-2},{"$f":"ASIN(J152/K152)","v":2.2187417132283428E-2},{"$f":"J153","v":2.2187417132283428E-2},{"$f":"ASIN(L152/M152)","v":2.1357745266052296E-2},{"$f":"L153","v":2.1357745266052296E-2},{"$f":"ASIN(N152/O152)","v":2.0681723129801152E-2},{"$f":"N153","v":2.0681723129801152E-2},{"$f":"ASIN(P152/Q152)","v":2.0533727014128388E-2},{"$f":"P153","v":2.0533727014128388E-2},{"$f":"ASIN(R152/S152)","v":2.2431614859781065E-2},{"$f":"R153","v":2.2431614859781065E-2},"sec incidence",{"$f":"ASIN(U152/V152)","v":2.2673585332548232E-2},{"$f":"U153","v":2.2673585332548232E-2},"sec incidence",null,null,null,null,0,-73.25,74.725260193250492,-6.4136954286131385,-8.5620512883261168E-2,-0.10937337891482861,-0.81534816911022756,-3,2.3752866031567441E-2,0,null,8,-0.10981160360726729,149.28762824042477,-14.601508632628612,-6.2917414282599822]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,-70.5,74.918724793411101,-3.4906554297335504,-4.6558891760877047E-2,-7.0428136463383709E-2,-0.77628654798784336,-3,2.3869244702506662E-2,0,null,19,-7.0544812018087211E-2,149.74345386483162,-8.7691518763812155,-4.041919995180165]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,-70.25,74.930406114959752,-3.2302073381136296,-4.3082757761560286E-2,-6.6960611232640493E-2,-0.77281041398852657,-3,2.3877853471080207E-2,0,null,20,-6.7060868668211746E-2,149.77299632425644,-8.2492164509280652,-3.8423047451696308]
["X1,Y1",{"$f":"IF(show_rays,IF(circle_left,B159,B197),0)","v":149.17828430524099},15.679269490148021,147.72116295183119,26.047226650039551,140.95389311788625,51.303021498850306,129.9038105676658,74.999999999999986,114.9066664678467,96.41814145298089,96.418141452980905,114.9066664678467,75.000000000000014,129.9038105676658,51.30302149885032,140.95389311788625,26.047226650039562,147.72116295183119,"X1,Y1",{"$f":"IF(circle_left,U159,U197)","v":124.35563588325624},83.878935520612032,"X1,Y1",{"$f":"IF(circle_left,X159,X197)","v":0},0,{"$f":"IF(circle_left,Z159,Z197)","v":0},{"$f":"IF(circle_left,AA159,AA197)","v":0},0,-70,74.941147135554957,-2.9706002772341833,-3.9618367147084242E-2,-6.3504515276271267E-2,-0.76934602337405056,-3,2.3886148129187025E-2,0,null,21,-6.359002070993218E-2,149.80064391988606,-7.7309172280848992,-3.6434398058286126]
["X2,Y2",{"$f":"IF(show_rays,IF(circle_left,B160,B198),0)","v":6.3062272092668972E-2},1.8058671962418089,6.3219758217075331E-2,1.8103770087888542,6.3637851002897608E-2,1.8223496196994209,6.4119097558527308E-2,1.8361307179579636,6.4718359898058395E-2,1.8532913460956886,6.5542328377415124E-2,1.8768867161676863,6.6844417173704429E-2,1.9141736607350737,6.9434100273635391E-2,1.988332481907183,7.8145090108572485E-2,2.2377825931653446,"X2,Y2",6.4340359054846794E-2,1.8424668182083255,"X2,Y2",0,0,{"$f":"IF(circle_left,Z160,Z198)","v":0},0,0,-69.75,74.950957304462221,-2.7118257954152369,-3.6165560534008379E-2,-6.0059692297962784E-2,-0.76589321676097466,-3,2.3894131763954406E-2,0,null,22,-6.013201175321977E-2,149.82641547481106,-7.2142377261423691,-3.4453104870905547]
["X3,Y3",{"$f":"IF(show_rays,IF(circle_left,B161,B199),0)","v":-76.619497167044358},-2.0378443668501292,-76.355118053947606,-5.5751035700221916,-74.994093566680874,-14.19647589857013,-72.749086032763742,-22.280195538066636,-69.846106312627271,-29.563314549540284,-66.606624047787264,-35.806316485998231,-63.439623944855342,-40.800361570824379,-60.81567671817723,-44.368358320357821,-59.248344088850089,-46.317739279089622,"X3,Y3",-71.650961471550389,-25.303544032340426,"X3,Y3",0,0,{"$f":"IF(circle_left,Z161,Z199)","v":0},0,0,-69.5,74.959845880883876,-2.4538756109744213,-3.2724181735649012E-2,-5.6625989135931011E-2,-0.7624518379626154,-3,2.3901807400281999E-2,0,null,23,-5.6686590659354531E-2,149.85032943315767,-6.6991617963832892,-3.2479023997667289]
["x4,y4",{"$f":"IF(show_rays,IF(circle_left,B162,B200),0)","v":-200.46418764257669},-9.8015819179824923,-200.7913024749173,-19.168925109486832,-201.61795211103896,-42.841073465696475,-202.45982971513661,-66.949293769850783,-203.31261622426226,-91.369904241426639,-204.15638867534801,-115.53238586386428,-204.94596717072602,-138.14295564425225,-205.60421306318563,-156.99265174316494,-206.03200442022759,-169.24299339566033,"x4,y4",-202.80030360653981,-76.699190360293088,"x4,y4",0,0,{"$f":"IF(circle_left,Z162,Z200)","v":0},0,0,-69.25,74.967821939214431,-2.196741607526576,-2.9294077671805106E-2,-5.3203255674368323E-2,-0.75902173389877148,-3,2.3909178002563217E-2,0,null,24,-5.3253511380620192E-2,149.87240387056818,-6.18567361386852,-3.0512014463614348]
["CIRCLE RIGHT",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CIRCLE RIGHT",null,null,"CIRCLE RIGHT","critical angle",{"$f":"ASIN(1/nn)","v":0.72972765622696634},null,null,0,-69,74.974894374109127,-1.9404158294501741,-2.587509828171471E-2,-4.979134475805988E-2,-0.75560275450868108,-3,2.391624647634517E-2,0,null,25,-4.9832532805927442E-2,149.89265650430835,-5.6737576685499951,-2.8551938122268603]
[null,6,6,10,{"$f":"D171","v":10},{"$f":"D171+10","v":20},{"$f":"F171","v":20},{"$f":"F171+10","v":30},{"$f":"H171","v":30},{"$f":"H171+10","v":40},{"$f":"J171","v":40},{"$f":"J171+10","v":50},{"$f":"L171","v":50},{"$f":"L171+10","v":60},{"$f":"N171","v":60},{"$f":"N171+10","v":70},{"$f":"P171","v":70},{"$f":"P171+10","v":80},{"$f":"R171","v":80},null,{"$f":"U133","v":34},{"$f":"U171","v":34},null,null,null,null,null,0,-68.75,74.98107190537344,-1.6848904775141307,-2.2467096440112005E-2,-4.6390112110042174E-2,-0.75219475266707836,-3,2.3923015669930169E-2,0,null,26,-4.6423418612110551E-2,149.91110470301834,-5.1633987566983732,-2.6598659570430083]
[null,{"$f":"RADIANS(B171)","v":0.10471975511965978},0.10471975511965978,0.17453292519943295,0.17453292519943295,0.3490658503988659,0.3490658503988659,0.52359877559829882,0.52359877559829882,0.69813170079773179,0.69813170079773179,0.87266462599716477,0.87266462599716477,1.0471975511965976,1.0471975511965976,1.2217304763960306,1.2217304763960306,1.3962634015954636,1.3962634015954636,null,0.59341194567807209,0.59341194567807209,null,null,null,null,null,0,-68.5,74.986363082681535,-1.4301579046573636,-1.9069927876241136E-2,-4.2999416252162019E-2,-0.74879758410320751,-3,2.3929488375920883E-2,0,null,27,-4.3025937120634725E-2,149.92776549612171,-4.6545819726302238,-2.4652046066076312]
["X1,Y1",{"$f":"150*COS(B172)","v":149.17828430524099},{"$f":"150*SIN(C172)","v":15.679269490148021},{"$f":"150*COS(D172)","v":147.72116295183119},{"$f":"150*SIN(E172)","v":26.047226650039551},{"$f":"150*COS(F172)","v":140.95389311788625},{"$f":"150*SIN(G172)","v":51.303021498850306},{"$f":"150*COS(H172)","v":129.9038105676658},{"$f":"150*SIN(I172)","v":74.999999999999986},{"$f":"150*COS(J172)","v":114.9066664678467},{"$f":"150*SIN(K172)","v":96.41814145298089},{"$f":"150*COS(L172)","v":96.418141452980905},{"$f":"150*SIN(M172)","v":114.9066664678467},{"$f":"150*COS(N172)","v":75.000000000000014},{"$f":"150*SIN(O172)","v":129.9038105676658},{"$f":"150*COS(P172)","v":51.30302149885032},{"$f":"150*SIN(Q172)","v":140.95389311788625},{"$f":"150*COS(R172)","v":26.047226650039562},{"$f":"150*SIN(S172)","v":147.72116295183119},"X1,Y1",{"$f":"150*COS(U172)","v":124.35563588325624},{"$f":"150*SIN(V172)","v":83.878935520612032},"X1,Y1",null,null,null,null,0,-68.25,74.990776290130626,-1.1762106119153799,-1.5683451095710555E-2,-3.9619118428422688E-2,-0.7454111073226769,-3,2.3935667332712133E-2,0,null,28,-3.9639861159486235E-2,149.94265558290783,-4.1472927007236393,-2.271196744923119]
[null,"we do a transformation by xc, yc ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,-68,74.994319750638297,-0.9230412444870808,-1.2307527305059332E-2,-3.6249082530990295E-2,-0.74203518353202569,-3,2.3941555225930965E-2,0,null,29,-3.6264967930009974E-2,149.95579134130094,-3.641516607708815,-2.0778296065668531]
[null,{"$f":"B173-XC","v":149.17828430524099},{"$f":"C173-YC","v":15.679269490148021},{"$f":"D173-XC","v":147.72116295183119},{"$f":"E173-YC","v":26.047226650039551},{"$f":"F173-XC","v":140.95389311788625},{"$f":"G173-YC","v":51.303021498850306},{"$f":"H173-XC","v":129.9038105676658},{"$f":"I173-YC","v":74.999999999999986},{"$f":"J173-XC","v":114.9066664678467},{"$f":"K173-YC","v":96.41814145298089},{"$f":"L173-XC","v":96.418141452980905},{"$f":"M173-YC","v":114.9066664678467},{"$f":"N173-XC","v":75.000000000000014},{"$f":"O173-YC","v":129.9038105676658},{"$f":"P173-XC","v":51.30302149885032},{"$f":"Q173-YC","v":140.95389311788625},{"$f":"R173-XC","v":26.047226650039562},{"$f":"S173-YC","v":147.72116295183119},null,{"$f":"U173-XC","v":124.35563588325624},{"$f":"V173-YC","v":83.878935520612032},null,null,null,null,null,0,-67.75,74.997001530189507,-0.67064258793621434,-8.9420203389250566E-3,-3.2889175028752597E-2,-0.73866967656589144,-3,2.3947154689827541E-2,0,null,30,-3.2901038878483599E-2,149.96718883632909,-3.1372396352227101,-1.8850906693329457]
["IN ROTATED","we do a transformation by gonia",null,null,null,"x11=x1cosg-y1singy11=x1sing+y1cosg",null,null,null,null,null,null,null,null,null,null,null,null,null,"IN ROTATED",null,null,"IN ROTATED",null,null,null,null,0,-67.5,74.998829541939344,-0.41900756452169219,-5.5867965897021402E-3,-2.9539264898320986E-2,-0.73531445281666852,-3,2.3952468308618847E-2,0,null,31,-2.9547859572221381E-2,149.97686382830585,-2.6344479926164492,-1.6929676471335151]
["X1,Y1",{"$f":"B175*COS(radiansg)-C175*SIN(radiansg)","v":148.54021031123554},{"$f":"B175*SIN(radiansg)+C175*COS(radiansg)","v":20.875965144009818},{"$f":"D175*COS(radiansg)-E175*SIN(radiansg)","v":146.72214011007082},{"$f":"D175*SIN(radiansg)+E175*COS(radiansg)","v":31.1867536226639},{"$f":"F175*COS(radiansg)-G175*SIN(radiansg)","v":139.07757818501813},{"$f":"F175*SIN(radiansg)+G175*COS(radiansg)","v":56.190989012386801},{"$f":"H175*COS(radiansg)-I175*SIN(radiansg)","v":127.20721442346391},{"$f":"H175*SIN(radiansg)+I175*COS(radiansg)","v":79.487889634980732},{"$f":"J175*COS(radiansg)-K175*SIN(radiansg)","v":111.47172382160915},{"$f":"J175*SIN(radiansg)+K175*COS(radiansg)","v":100.36959095382872},{"$f":"L175*COS(radiansg)-M175*SIN(radiansg)","v":92.349221298848747},{"$f":"L175*SIN(radiansg)+M175*COS(radiansg)","v":118.2016130410083},{"$f":"N175*COS(radiansg)-O175*SIN(radiansg)","v":70.420734417883622},{"$f":"N175*SIN(radiansg)+O175*COS(radiansg)","v":132.44213892883906},{"$f":"P175*COS(radiansg)-Q175*SIN(radiansg)","v":46.352549156242127},{"$f":"P175*SIN(radiansg)+Q175*COS(radiansg)","v":142.65847744427305},{"$f":"R175*COS(radiansg)-S175*SIN(radiansg)","v":20.875965144009829},{"$f":"R175*SIN(radiansg)+S175*COS(radiansg)","v":148.54021031123551},"X1,Y1",{"$f":"U175*COS(radiansg)-V175*SIN(radiansg)","v":121.35254915624211},{"$f":"U175*SIN(radiansg)+V175*COS(radiansg)","v":88.167787843870983},"X1,Y1",{"$f":"150*COS(critical_angle)","v":111.80339887498948},{"$f":"150*SIN(critical_angle)","v":100},{"$f":"AS143","v":111.49408423103117},{"$f":"AU143","v":100.34475163895581},0,-67.25,74.999811550177483,-0.1681292296517114,-2.2417249395905421E-3,-2.6199223557377558E-2,-0.73196938116655685,-3,2.3957498617787017E-2,0,null,32,-2.6205219580017126E-2,149.9848317807359,-2.133128150005521,-1.501448483148569]
[null,"we find the point at which the line from x1, y1 meets the radius",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,-67,74.999955174160121,8.1999231543647966E-2,1.0933233050670276E-3,{"$f":"ATAN((AE178-htry)/(AD178-htrx))","v":-2.2868924800267247E-2},-0.72863433292189927,-1.5213348385969314,2.3962248105334275E-2,0,null,33,-2.287291235673819E-2,149.99110786795646,-1.6332668315523267,-1.3105213432137275]
[null,"the point y at whih it cuts the diameter is (0,h) in lab so it is (-xc, h-yc) in the fist trnsforamtion and it is (htrx, htry) by the second transformation",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,-66.75,74.999267891814597,0.33138450752591098,4.4184744772496429E-3,-1.9548244735746588E-2,-0.7253091817497167,-1.4712590096877096,2.3966719212996229E-2,0,null,34,-1.9550735131898683E-2,149.99570698252481,-1.1348510089721369,-1.1201746094359393]
["X=0,Y=h",{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},"X=0,Y=h",{"$f":"htrx","v":-6.2819094064501743E-2},{"$f":"htry","v":1.7989034886343724},"X=0,Y=h",null,null,null,null,0,-66.5,74.997757043322153,0.580033163552784,7.733852610619092E-3,-1.6237061726796037E-2,-0.72199380361634724,-1.438969879405761,2.397091433741513E-2,0,null,35,-1.6238488802039524E-2,149.99864374236256,-0.63786789525261889,-0.93039687402731286]
["KLISI out",{"$f":"ATAN((C177-htry)/(B177-htrx))","v":0.12767765764707673},{"$f":"B181","v":0.12767765764707673},{"$f":"ATAN((E177-htry)/(D177-htrx))","v":0.19759769388327875},{"$f":"D181","v":0.19759769388327875},{"$f":"ATAN((G177-htry)/(F177-htrx))","v":0.37265013639487443},{"$f":"F181","v":0.37265013639487443},{"$f":"ATAN((I177-htry)/(H177-htrx))","v":0.54805070649626975},{"$f":"H181","v":0.54805070649626975},{"$f":"ATAN((K177-htry)/(J177-htrx))","v":0.7237745601822031},{"$f":"J181","v":0.7237745601822031},{"$f":"ATAN((M177-htry)/(L177-htrx))","v":0.8997863529763882},{"$f":"L181","v":0.8997863529763882},{"$f":"ATAN((O177-htry)/(N177-htrx))","v":1.0760412018930554},{"$f":"N181","v":1.0760412018930554},{"$f":"ATAN((Q177-htry)/(P177-htrx))","v":1.2524860350227911},{"$f":"P181","v":1.2524860350227911},{"$f":"ATAN((S177-htry)/(R177-htrx))","v":1.4290612916822574},{"$f":"R181","v":1.4290612916822574},"KLISI out",{"$f":"ATAN2(U177-htrx,V177-htry)","v":0.61830320650295456},{"$f":"U181","v":0.61830320650295456},"KLISI out",{"$f":"TAN(U181)","v":0.71135051188232523},null,null,null,0,-66.25,74.995429834583334,0.82795164477765582,1.1039579498854969E-2,-1.2935256332419777E-2,-0.71868807672811141,-1.4131319019331956,2.3974835831274743E-2,0,null,36,-1.2935977826763938E-2,149.99993249766632,-0.14230493857944237,-0.74117693334838841]
["DEGREES",{"$f":"DEGREES(B181)","v":7.3153909212937176},{"$f":"B182","v":7.3153909212937176},{"$f":"DEGREES(D181)","v":11.321513901029874},{"$f":"D182","v":11.321513901029874},{"$f":"DEGREES(F181)","v":21.351280050400781},{"$f":"F182","v":21.351280050400781},{"$f":"DEGREES(H181)","v":31.400992441399264},{"$f":"H182","v":31.400992441399264},{"$f":"DEGREES(J181)","v":41.469227617377641},{"$f":"J182","v":41.469227617377641},{"$f":"DEGREES(L181)","v":51.553960489015601},{"$f":"L182","v":51.553960489015601},{"$f":"DEGREES(N181)","v":61.652619450656601},{"$f":"N182","v":61.652619450656601},{"$f":"DEGREES(P181)","v":71.762163705880539},{"$f":"P182","v":71.762163705880539},{"$f":"DEGREES(R181)","v":81.879180678907247},{"$f":"R182","v":81.879180678907247},"DEGREES",{"$f":"DEGREES(U181)","v":35.426164192025091},{"$f":"U182","v":35.426164192025091},"DEGREES",null,null,null,null,0,-66,74.992293340570797,1.075146279248429,1.4335774753048069E-2,-9.6427112513503867E-3,-0.7153918814739183,-1.3909428270024187,2.3978486004398454E-2,0,null,37,-9.6430101282741522E-3,149.99958733759348,0.35185018354070219,-0.55250378215201557]
[null,"we find the point at which the line from x1, y1 meets the CIRCLE y =y1+tan(klisi)*(x-x1)  y^2+x^2=R^2",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,-65.75,74.988354508574346,1.3216232808100301,1.7622555857234139E-2,-6.3593112675776609E-3,-0.71210510036973218,-1.3711820189111912,2.39818671248118E-2,0,null,38,-6.3593969942604706E-3,149.99762209673298,0.84460956996821479,-0.36436660801930637]
[null,{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(B181))^2)-(B177*TAN(B181)-C177)^2","v":5714.4370938221909},{"$f":"B184","v":5714.4370938221909},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(D181))^2)-(D177*TAN(D181)-E177)^2","v":5847.1917997164064},{"$f":"D184","v":5847.1917997164064},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(F181))^2)-(F177*TAN(F181)-G177)^2","v":6481.2573051322306},{"$f":"F184","v":6481.2573051322306},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(H181))^2)-(H177*TAN(H181)-I177)^2","v":7717.6140844929405},{"$f":"H184","v":7717.6140844929405},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(J181))^2)-(J177*TAN(J181)-K177)^2","v":10014.946640597034},{"$f":"J184","v":10014.946640597034},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(L181))^2)-(L177*TAN(L181)-M177)^2","v":14546.131103450778},{"$f":"L184","v":14546.131103450778},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(N181))^2)-(N177*TAN(N181)-O177)^2","v":24946.389142912165},{"$f":"N184","v":24946.389142912165},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(P181))^2)-(P177*TAN(P181)-Q177)^2","v":57426.040389446709},{"$f":"P184","v":57426.040389446709},{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(R181))^2)-(R177*TAN(R181)-S177)^2","v":281884.032305534},{"$f":"R184","v":281884.032305534},null,{"$f":"RADIUS_OF_SEMICIRCLE^2*(1+(TAN(U181))^2)-(U177*TAN(U181)-V177)^2","v":8467.9611493402572},{"$f":"U184","v":8467.9611493402572},"CUT SEMICIRCLE",null,null,null,null,0,-65.5,74.983620161341733,1.5673887519135405,2.0900038222130317E-2,-3.08494319764084E-3,-0.70882761800483607,-1.3531868814697332,2.3984981419771158E-2,0,null,39,-3.0849529840172116E-3,149.99405036136847,1.3359851014355533,-0.17675478598047553]
["X2,Y2",{"$f":"(TAN(B181)*(B177*TAN(B181)-C177)+SQRT(B184))/(1+(TAN(B181))^2)","v":74.140066913545496},{"$f":"C177+TAN(C181)*(B185-B177)","v":11.324772759530168},{"$f":"(TAN(D181)*(D177*TAN(D181)-E177)+SQRT(D184))/(1+(TAN(D181))^2)","v":73.171249524259025},{"$f":"E177+TAN(E181)*(D185-D177)","v":16.461113056492426},{"$f":"(TAN(F181)*(F177*TAN(F181)-G177)+SQRT(F184))/(1+(TAN(F181))^2)","v":69.216191173449658},{"$f":"G177+TAN(G181)*(F185-F177)","v":28.8811163122285},{"$f":"(TAN(H181)*(H177*TAN(H181)-I177)+SQRT(H184))/(1+(TAN(H181))^2)","v":63.18458350338237},{"$f":"I177+TAN(I181)*(H185-H177)","v":40.406786651552736},{"$f":"(TAN(J181)*(J177*TAN(J181)-K177)+SQRT(J184))/(1+(TAN(J181))^2)","v":55.26853855758516},{"$f":"K177+TAN(K181)*(J185-J177)","v":50.699000440923093},{"$f":"(TAN(L181)*(L177*TAN(L181)-M177)+SQRT(L184))/(1+(TAN(L181))^2)","v":45.713096675164152},{"$f":"M177+TAN(M181)*(L185-L177)","v":59.458496385017128},{"$f":"(TAN(N181)*(N177*TAN(N181)-O177)+SQRT(N184))/(1+(TAN(N181))^2)","v":34.80821371553597},{"$f":"O177+TAN(O181)*(N185-N177)","v":66.433336947150039},{"$f":"(TAN(P181)*(P177*TAN(P181)-Q177)+SQRT(P184))/(1+(TAN(P181))^2)","v":22.87998109041899},{"$f":"Q177+TAN(Q181)*(P185-P177)","v":71.424830873457921},{"$f":"(TAN(R181)*(R177*TAN(R181)-S177)+SQRT(R184))/(1+(TAN(R181))^2)","v":10.281345788829736},{"$f":"S177+TAN(S181)*(R185-R177)","v":74.291950632423919},"X2,Y2",{"$f":"(TAN(U181)*(U177*TAN(U181)-V177)+SQRT(U184))/(1+(TAN(U181))^2)","v":60.231679472319875},{"$f":"V177+TAN(V181)*(U185-U177)","v":44.689425907520011},"X2,Y2",null,{"$f":"RADIUS_OF_SEMICIRCLE*SIN(critical_angle)","v":50},{"$f":"AD133","v":55.279746643512802},{"$f":"AE133","v":50.686779450158731},0,-65.25,74.978097000119959,1.8124486863365092,2.4168335237156943E-2,1.8050416039734052E-4,-0.70555932098980945,-1.3365500757511415,2.3987831076759603E-2,0,null,40,1.8050416235772113E-4,149.98888547554287,1.8259884458780578,1.0342126687641603E-2]
["exterior prod",{"$f":"B185*(C177-C185)-C185*(B177-B185)","v":-134.43867476583102},{"$f":"SQRT((B185-B177)^2+(C185-C177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.8032494291238},{"$f":"D185*(E177-E185)-E185*(D177-D185)","v":-133.23600506686853},{"$f":"SQRT((D185-D177)^2+(E185-E177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.7889426979045},{"$f":"F185*(G177-G185)-G185*(F177-F185)","v":-127.38947427798735},{"$f":"SQRT((F185-F177)^2+(G185-G177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.7212248025917},{"$f":"H185*(I177-I185)-I185*(H177-H185)","v":-117.62557359814627},{"$f":"SQRT((H185-H177)^2+(I185-I177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.6149065553582},{"$f":"J185*(K177-K185)-K185*(J177-J185)","v":-104.22436754148612},{"$f":"SQRT((J185-J177)^2+(K185-K177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.4827771438077},{"$f":"L185*(M177-M185)-M185*(L177-L185)","v":-87.584076652788553},{"$f":"SQRT((L185-L177)^2+(M185-M177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.340926855959},{"$f":"N185*(O177-O185)-O185*(N177-N185)","v":-68.210100871292525},{"$f":"SQRT((N185-N177)^2+(O185-O177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.2067811157367},{"$f":"P185*(Q177-Q185)-Q185*(P177-P185)","v":-46.69971772530721},{"$f":"SQRT((P185-P177)^2+(Q185-Q177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.0969268551562},{"$f":"R185*(S177-S185)-S185*(R177-R185)","v":-23.722906127676197},{"$f":"SQRT((R185-R177)^2+(S185-S177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.0250122510888},"exterior prod",{"$f":"U185*(V177-V185)-V185*(U177-U185)","v":-112.68181701102367},{"$f":"SQRT((U185-U177)^2+(V185-V177)^2)*RADIUS_OF_SEMICIRCLE","v":5625.5643054878292},"exterior prod",null,null,null,null,0,-65,74.971791607600338,2.0568089718170341,2.7427558320800228E-2,3.437140076348804E-3,-0.7023000979061661,-1.3209999962738197,2.3990418244451424E-2,0,null,41,3.4371536117923695E-3,149.98214054693128,2.3146310635956615,0.19693439549385014]
["incd=asin(ext)",{"$f":"ATAN2(B185,C185)-ATAN2(B177-B185,C177-C185)","v":2.3899071376813463E-2},{"$f":"B187","v":2.3899071376813463E-2},{"$f":"ATAN2(D185,E185)-ATAN2(D177-D185,E177-E185)","v":2.3685293681211667E-2},{"$f":"D187","v":2.3685293681211667E-2},{"$f":"ATAN2(F185,G185)-ATAN2(F177-F185,G177-G185)","v":2.264604986943064E-2},{"$f":"F187","v":2.264604986943064E-2},{"$f":"ATAN2(H185,I185)-ATAN2(H177-H185,I177-I185)","v":2.0910451193987711E-2},{"$f":"H187","v":2.0910451193987711E-2},{"$f":"ATAN2(J185,K185)-ATAN2(J177-J185,K177-K185)","v":1.8528246411802285E-2},{"$f":"J187","v":1.8528246411802285E-2},{"$f":"ATAN2(L185,M185)-ATAN2(L177-L185,M177-M185)","v":1.5570187965025073E-2},{"$f":"L187","v":1.5570187965025073E-2},{"$f":"ATAN2(N185,O185)-ATAN2(N177-N185,O177-O185)","v":1.2126091569647501E-2},{"$f":"N187","v":1.2126091569647501E-2},{"$f":"ATAN2(P185,Q185)-ATAN2(P177-P185,Q177-Q185)","v":8.3021243548295764E-3},{"$f":"P187","v":8.3021243548295764E-3},{"$f":"ATAN2(R185,S185)-ATAN2(R177-R185,S177-S185)","v":4.2173992827696516E-3},{"$f":"R187","v":4.2173992827696516E-3},"incd=asin(ext)",{"$f":"ATAN2(U185,V185)-ATAN2(U177-U185,V177-V185)","v":2.0031653210705325E-2},{"$f":"U187","v":2.0031653210705325E-2},"incd=asin(ext)",{"$f":"ASIN(U186/V186)","v":-2.0031653210705349E-2},null,null,null,0,-64.75,74.964710450771534,2.3004753926056196,3.0677816969389118E-2,6.6850719357427618E-3,-0.69904983925757724,-1.3063448166748517,2.3992745033646356E-2,0,null,42,6.685171523227491E-3,149.97382845252963,2.8019242122533834,0.38303211360197903]
["refraction=",{"$f":"ASIN(SIN(B187)/nn)","v":1.593187156619269E-2},{"$f":"B188","v":1.593187156619269E-2},{"$f":"ASIN(SIN(D187)/nn)","v":1.5789375515540119E-2},{"$f":"D188","v":1.5789375515540119E-2},{"$f":"ASIN(SIN(F187)/nn)","v":1.5096649618225176E-2},{"$f":"F188","v":1.5096649618225176E-2},{"$f":"ASIN(SIN(H187)/nn)","v":1.3939736374319981E-2},{"$f":"H188","v":1.3939736374319981E-2},{"$f":"ASIN(SIN(J187)/nn)","v":1.2351771620284805E-2},{"$f":"J188","v":1.2351771620284805E-2},{"$f":"ASIN(SIN(L187)/nn)","v":1.0379892295839953E-2},{"$f":"L188","v":1.0379892295839953E-2},{"$f":"ASIN(SIN(N187)/nn)","v":8.083950979440464E-3},{"$f":"N188","v":8.083950979440464E-3},{"$f":"ASIN(SIN(P187)/nn)","v":5.5347142469191653E-3},{"$f":"P188","v":5.5347142469191653E-3},{"$f":"ASIN(SIN(R187)/nn)","v":2.8115948914273045E-3},2.8115948914273045E-3,"refraction=",{"$f":"ASIN(SIN(U187)/nn)","v":1.3353939268382627E-2},1.3353939268382627E-2,"refraction=",{"$f":"ASIN(SIN(X187)/nn)","v":-1.3353939268382645E-2},null,null,null,0,-64.5,74.956859883683663,2.543453631937453,3.3919218804340658E-2,9.9244052861659198E-3,-0.69580843742262566,-1.2924431009726531,2.3994813518174736E-2,0,null,43,9.9247311298669236E-3,149.96396184416707,3.2878789517257649,0.56864520654347961]
["interior klisi",{"$f":"ATAN2(B185,C185)-B188","v":0.1356448574576975},{"$f":"B189","v":0.1356448574576975},{"$f":"ATAN2(D185,E185)-D188","v":0.20549361204895028},{"$f":"D189","v":0.20549361204895028},{"$f":"ATAN2(F185,G185)-F188","v":0.38019953664607992},{"$f":"F189","v":0.38019953664607992},{"$f":"ATAN2(H185,I185)-H188","v":0.55502142131593746},{"$f":"H189","v":0.55502142131593746},{"$f":"ATAN2(J185,K185)-J188","v":0.7299510349737206},{"$f":"J189","v":0.7299510349737206},{"$f":"ATAN2(L185,M185)-L188","v":0.90497664864557337},{"$f":"L189","v":0.90497664864557337},{"$f":"ATAN2(N185,O185)-N188","v":1.0800833424832625},{"$f":"N189","v":1.0800833424832625},{"$f":"ATAN2(P185,Q185)-P188","v":1.2552534451307016},{"$f":"P189","v":1.2552534451307016},{"$f":"ATAN2(R185,S185)-R188","v":1.4304670960735997},1.4304670960735997,"interior klisi",{"$f":"ATAN2(U185,V185)-U188","v":0.62498092044527731},0.62498092044527731,"interior klisi",null,null,null,null,0,-64.25,74.948246150126963,2.7857492744283121,3.7151869617934957E-2,1.3155243882160208E-2,-0.69257578660903141,-1.2791870212954466,2.3996625735774747E-2,0,null,44,1.3156002818802212E-2,149.95255315384708,3.7725061487915603,0.75378343677958104]
["X3,Y3",0,{"$f":"C185+TAN(C189)*(B190-B185)","v":1.2059169703342807},0,{"$f":"E185+TAN(E189)*(D190-D185)","v":1.209603556478184},0,{"$f":"G185+TAN(G189)*(F190-F185)","v":1.219273281121442},0,{"$f":"I185+TAN(I189)*(H190-H185)","v":1.2300973211173556},0,{"$f":"K185+TAN(K189)*(J190-J185)","v":1.2430898365931},0,{"$f":"M185+TAN(M189)*(L190-L185)","v":1.2602767889112414},0,{"$f":"O185+TAN(O189)*(N190-N185)","v":1.2865431721389342},0,{"$f":"Q185+TAN(Q189)*(P190-P185)","v":1.3376018351552119},0,{"$f":"S185+TAN(S189)*(R190-R185)","v":1.5076190095182938},"X3,Y3",0,{"$f":"V185+TAN(V189)*(U190-U185)","v":1.2349536840789668},"X3,Y3",{"$f":"0","v":0},{"$f":"0","v":0},{"$f":"0","v":0},{"$f":"AC127","v":1.2430711841385302},0,-64,74.938875386228489,3.0273678083970879,4.0375873417676719E-2,1.6377689728734067E-2,-0.68935178280928966,-1.2664921426622611,2.3998183688942652E-2,0,null,45,1.6379154208115917E-2,149.93961459892517,4.2558164816845334,0.93845640811898401]
["refra out",{"$f":"IF(SIN(B189)*nn<1,ASIN(SIN(B189)*nn),-B189)","v":0.20426133835546328},{"$f":"B191","v":0.20426133835546328},{"$f":"IF(SIN(D189)*nn<1,ASIN(SIN(D189)*nn),-D189)","v":0.31106806570509077},{"$f":"D191","v":0.31106806570509077},{"$f":"IF(SIN(F189)*nn<1,ASIN(SIN(F189)*nn),-F189)","v":0.59035822024275197},{"$f":"F191","v":0.59035822024275197},{"$f":"IF(SIN(H189)*nn<1,ASIN(SIN(H189)*nn),-H189)","v":0.91153067401096488},{"$f":"H191","v":0.91153067401096488},{"$f":"IF(SIN(J189)*nn<1,ASIN(SIN(J189)*nn),-J189)","v":-0.7299510349737206},{"$f":"J191","v":-0.7299510349737206},{"$f":"IF(SIN(L189)*nn<1,ASIN(SIN(L189)*nn),-L189)","v":-0.90497664864557337},{"$f":"L191","v":-0.90497664864557337},{"$f":"IF(SIN(N189)*nn<1,ASIN(SIN(N189)*nn),-N189)","v":-1.0800833424832625},{"$f":"N191","v":-1.0800833424832625},{"$f":"IF(SIN(P189)*nn<1,ASIN(SIN(P189)*nn),-P189)","v":-1.2552534451307016},{"$f":"P191","v":-1.2552534451307016},{"$f":"IF(SIN(R189)*nn<1,ASIN(SIN(R189)*nn),-R189)","v":-1.4304670960735997},{"$f":"R191","v":-1.4304670960735997},"refra out",{"$f":"IF(SIN(U189)*nn<1,ASIN(SIN(U189)*nn),-U189)","v":1.0708800545286952},{"$f":"U191","v":1.0708800545286952},"refra out",null,null,null,null,0,-63.75,74.92875362296931,3.26831462811721,4.3591332469290617E-2,1.9591843123533514E-2,-0.68613632375767575,-1.2542908831769315,2.3999489345757102E-2,0,null,46,1.9594350221555906E-2,149.92515818712894,4.7378204445048473,1.122673569996383]
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["out klisi",{"$f":"B191","v":0.20426133835546328},{"$f":"B193","v":0.20426133835546328},{"$f":"D191","v":0.31106806570509077},{"$f":"D193","v":0.31106806570509077},{"$f":"F191","v":0.59035822024275197},{"$f":"F193","v":0.59035822024275197},{"$f":"H191","v":0.91153067401096488},{"$f":"H193","v":0.91153067401096488},{"$f":"J191","v":-0.7299510349737206},{"$f":"J193","v":-0.7299510349737206},{"$f":"L191","v":-0.90497664864557337},{"$f":"L193","v":-0.90497664864557337},{"$f":"N191","v":-1.0800833424832625},{"$f":"N193","v":-1.0800833424832625},{"$f":"P191","v":-1.2552534451307016},{"$f":"P193","v":-1.2552534451307016},{"$f":"R191","v":-1.4304670960735997},{"$f":"R193","v":-1.4304670960735997},"out klisi",{"$f":"U191","v":1.0708800545286952},{"$f":"U193","v":1.0708800545286952},"out klisi",null,null,null,null,0,-63.25,74.906280711137455,3.74821424471385,4.9997016931002572E-2,2.5995665455677712E-2,-0.67973063929596378,-1.2311583400939319,2.400135147532486E-2,0,null,48,2.6001522775977344E-2,149.89173880474269,5.6979503412018211,1.4897775159767861]
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