{"text_format":"1","workbook":"xlsx","n_sheets":11,"sheets":["INTRODUCTION","SPHERICAL LENSES","THICK LENS MODEL","STANDARD DEVIATION OF Y OVER X","IMAGE VS b","FIND_F","graph_cuts","hUYGEN LENS CLOSED","HUG_METH","hyperbola","spherical"],"not_rendered":{"charts":23,"images":65,"macros":1,"external_links":0,"defined_names":264,"comments":0,"pivot_tables":0},"unopened":[{"sheet":"SPHERICAL LENSES","index":1,"reason":"not_a_worksheet"},{"sheet":"THICK LENS MODEL","index":2,"reason":"not_a_worksheet"},{"sheet":"STANDARD DEVIATION OF Y OVER X","index":3,"reason":"not_a_worksheet"},{"sheet":"IMAGE VS b","index":4,"reason":"not_a_worksheet"},{"sheet":"hUYGEN LENS CLOSED","index":7,"reason":"not_a_worksheet"}],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"INTRODUCTION","index":0,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"FIND_F","index":5,"n_rows":48,"n_cols":58,"rows_kept":48,"cut":false,"hidden":false,"merged":[]}
["Object","Image","A",616.98184181111719,null,null,null,null,null,null,null,null,null,null,null,null," k  = 8,469",270.55077755498883,"a",12,null,"b","1/a","1/b","sx^2","Sxy","Sy²","Sy²",null,null,null,null,"POINTS OF 1/b vs 1/a using the paraxial theory",null,null,null,null,null,"L",{"$f":"h_2*h_1-F_LENGTH*h_2+F_LENGTH*h_1","v":-3446.3787022999322},null,null,null,null,null,null,null,"bbi","si","aai","sobject",null,"dcut2",2.8024024906181627E-4,{"$f":"f_1","v":-158.0793290106528},null,null,"dxcut = -1 / (F_1 + H1) / 20"]
[-246.71348243190027,542.68788589822429,246.71348243190027,789.40136833012457,-3.6392507427780578,null,null,null,null,null,null,null,{"$f":"f_1","v":-158.0793290106528},{"$f":"h_1+f_1","v":-185.95336069639959},null,null," t  = -0,19",-7.4664709928433243E-2,null,{"$f":"h_2","v":-3.2715356037506851},{"$f":"-ysource/f_2","v":-0.21086459274562735},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1/(h_2+f_2/(1+f_1/(h_1+$C2)))","v":1.4706903741056921E-3},null,null,{"$f":"1/10000","v":1E-4},{"$f":"1/AV2","v":5.3641260140630679E-3},{"$f":"ap+bp*AS2+cp*AS2^2","v":6.0360273181000726E-3},{"$f":"dcut2*(AZ2-1)","v":0},null,null,{"$f":"f_2+h_2","v":186.42365920903265},100000,100000,{"$f":"f_2+h_2","v":186.42365920903265},1,"ap",6.0360273181000726E-3,{"$f":"f_1/AY2","v":-0.84795744103167725},{"$f":"f_2/(1+BC2)","v":1247.6453704801518},null,{"$f":"-1/(f_1+h_1)/20","v":2.6888462683733632E-4}]
[-303.647362993108,370.5162740234037,303.647362993108,674.16363701651176,-2.3657384612208574,null,null,null,null,null,null,null,{"$f":"F_LEFT","v":-185.95336069639959},null,null,160,8.4685336815551615,null,"1,8E+02 = B",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.2664915789024549E-3,0,5.8301830212788555E-3,{"$f":"(AZ3-1)*dxcut","v":2.6888462683733632E-4},{"$f":"((h_1+f_1)/AX3+1)/((h_1*h_2+f_1*h_2+f_2*h_1)/AX3+h_2+f_2)","v":5.1305456613224441E-3},5.7750851209944914E-3,2.8024024906181627E-4,null,null,{"$f":"AW3+h_2","v":194.77920194357534},{"$f":"IF(1+f_1/AY3<>0,f_2/(1+f_1/AY3),100000)","v":198.05073754732604},{"$f":"1/(dxcut*(AZ3-1))","v":3719.0672139279914},{"$f":"AX3-h_1","v":3746.9412456137384},{"$f":"AZ2+1","v":2},"bp",-0.92346376155305498,-4.2188899864844254E-2,198.05073754732604]
[-360.58124355431573,306.29240339846348,360.58124355431573,666.87364695277915,-1.5986266589148943,null,null,null,null,null,null,null,null,null,null,330,"1,6E+02 = B",null,"163,710555623235 =G",{"$f":"-ysource/f_2","v":-0.21086459274562735},{"$f":"F_LEFT","v":-185.95336069639959},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.7921850546496797E-3,6.1812125482700068E-3,0,5.3776925367467264E-4,4.8937693110705288E-3,5.5098419587521303E-3,5.6048049812363254E-4,null,null,203.76385363331067,207.03538923706137,1859.5336069639957,1887.4076386497425,{"$f":"AZ3+1","v":3},"cp",-27.382614099009153,-8.3754736270826621E-2,207.03538923706137]
[-417.51512411552352,272.80546808599331,417.51512411552352,690.32059220151677,-1.2063007813129347,null,null,null,null,null,null,null,null,null,null,{"$f":"Q3","v":8.4685336815551615},null,null,null,{"$f":"ABS(f_1)+ABS(h_1)","v":185.95336069639959},{"$f":"f_1","v":-158.0793290106528},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"1/(h_2+f_2/(1+f_1/(h_1+RC3)))",null,null,3.1653371997537416E-3,null,null,8.0665388051200896E-4,4.6537309169038974E-3,5.2402978313729866E-3,8.4072074718544881E-4,null,null,213.45144439678685,216.72298000053755,1239.6890713093305,1267.5631029950773,4,"dxcut",{"$f":"-1/(f_1+h_1)/20","v":2.6888462683733632E-4},-0.12471121054023511,216.72298000053755]
[-474.44900467673131,252.06330689851126,474.44900467673131,726.51231157524262,-0.96927576759899292,null,null,null,null,null,{"$f":"\"from the chart a+b vs a we get from the perp asymptote f_1+h_ = \"& TEXT(nlysh,\"0,00\") & \" from the other asymptote f_2+h_2 = \" & TEXT(llysh-nlysh,\"0,00\")","v":"from the chart a+b vs a we get from the perp asymptote f_1+h_ = -178,92 from the other asymptote f_2+h_2 = 165,47"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.4439303489590452E-3,{"$f":"1/AN4","v":161.78055554486301},{"$f":"1/AO3","v":171.52120205321603},1.0755385073493453E-3,4.4103625999670857E-3,4.966452738857062E-3,1.1209609962472651E-3,null,null,223.92782728319989,227.19936288695058,929.76680348199784,957.64083516774463,5,null,null,-0.16507162519125756,227.19936288695058]
[-531.38288523793904,238.0685327735232,531.38288523793904,769.45141801146224,-0.81103888897304055,null,null,null,null,null," From the Hyperbolic fit we find from the ASYMPTOTE cut of A+B axis: FOCAL LENGTH = 165,47 we find that minimum of HYPERBOLA: 2(|F1|+|H1|)= 338,85 4(|F1|+|H1|)= 664,25 (ON THE GRAPH THE RED LINE). The ratio of minimum to a = 1,96",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.6598653017883504E-3,{"$f":"f_2","v":189.69519481278334},{"$f":"f_1","v":-158.0793290106528},1.3444231341866817E-3,4.1635945849571639E-3,4.6883066812043557E-3,1.4012012453090813E-3,null,null,235.29342949220893,238.56496509595962,743.81344278559823,771.68747447134501,6,null,null,-0.20484889834313716,238.56496509595962]
[-588.31676579914676,227.89369411281746,588.31676579914676,816.21045991196422,-0.69599921881579907,"cut x = 0,0118f_left = 85,06",null,null," the dashed line meets the x axis  at 5,24E-03 so f = 190,7 and the y axis at 5,87E-03 f right = 170,39",null,null,null,null,null,null,null,null,null,null,null,null,null,null,338.84832983395671,null,null,null,"ap + bp * ActiveSheet.Cells(ii + 1, 45).Value + cp * (ActiveSheet.Cells(ii + 1, 45).Value) ^ 2",null,null,null,null,null,null,null,null,null,null,3.8321438382338049E-3,null,null,1.6133077610240179E-3,3.9133551334275176E-3,4.4058596584148685E-3,1.6814414943708976E-3,null,null,247.66648201637162,250.93801762012231,619.84453565466526,647.71856734041205,7,null,"SOBJECT = AII1 - H1",-0.24405557750141404,250.93801762012231]
[-645.25064636035449,220.32506511728818,645.25064636035449,865.5757114776427,-0.60990819309567068,null,null,null," The dotted line is the linear trend line for the data and meets the y axis at 6,18E-03 and the x axis at 5,83E-03 so   f RIGHT+h2 =  161,78 , |f LEFT|+|h1| = 171,52 The Green Lines is the parabolic trend line with  y cut at 6,04E-03x cut at 5,60E-03 with corresponding f RIGHT+h2 = 165,67  |f LEFT+|h1| = 178,42",null,null,null,null,null,null,null,null,null,null,null,null,null,null,684.79076350122307,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.9727897891737559E-3,null,null,1.8821923878613541E-3,3.6595704742569306E-3,4.1191116704886004E-3,1.9616817434327137E-3,null,null,261.18714794159331,264.458683545344,531.29531627542735,559.16934796117414,8,null,"If ii = 1 Then",-0.28270385275415527,264.458683545344]
[-702.18452692156234,214.16057589854313,702.18452692156234,916.34510282010547,-0.54307244331830207,"ap = 3,48E-03f-right = 287,54",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"AMIn = 353,36 VAL= 684,79",null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.0897828035174385E-3,null,null,2.1510770146986906E-3,3.402164731142388E-3,3.8280627174255488E-3,2.2419219924945302E-3,null,null,276.02285532276545,279.29439092651614,464.88340174099892,492.75743342674571,9,null,"bbii = F_2 + H2",-0.32080556940832672,279.29439092651614]
[-759.11840748277007,209.57898452354712,759.11840748277007,968.69739200631716,-0.48968849685611748,"bp = -5,70E-01",null,null,"The cut on X- Axos  is 0,0056 f = 178,42",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,4.1886267757962978E-3,null,null,2.419961641536027E-3,3.14105984696591E-3,3.5327127992257176E-3,2.5221622415563466E-3,null,null,292.37526565142252,295.64680125517322,413.22969043644349,441.10372212219028,10,null,null,-0.35837224009382357,295.64680125517322]
[-816.0522880439778,205.7167733985504,816.0522880439778,1021.7690614425283,-0.44512607221250217,"cp = -1,13E+01",null,null,null,null,null,null,null,null,null,null,null,"R1",null,null,null,null,null,null,null,null,"value ata amin",null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.6888462683733634E-3,2.8761755048770494E-3,3.2330619158891048E-3,2.8024024906181627E-3,null,null,310.48949468431988,313.76103028807057,371.90672139279911,399.7807530785459,11,null,"Else",-0.39541505636114144,313.76103028807057]
[-872.98616860518553,202.33159746105309,872.98616860518553,1075.3177660662386,-0.40888241785875601,null,null,null,null,null,null,null,null,null,null,null,null,"R2",null,null,null,null,null,null,null,null,{"$f":"2*SQRT(Y13)+f_2+h_2-f_1-h_1","v":372.37701990543223},null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.9577308952106994E-3,2.6074290459234448E-3,2.9291100674157101E-3,3.0826427396799787E-3,null,null,330.66648334031066,333.93801894406135,338.09701944799923,365.97105113374602,12,null,"If 1 + F_1 / SOBJECT <> 0 Then",-0.43194489979722983,333.93801894406135]
[null,null,487.08845849591887,594.12210034173677,-0.37741970771540634,{"$f":"f_1","v":-158.0793290106528},null,null,null,null,null,null,null,null,null,null,null,"width",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.2266155220480358E-3,2.3347353830519713E-3,2.6208572538055346E-3,3.3628829887417952E-3,null,null,353.27984996673831,356.551385570489,309.92226782733263,337.79629951307942,13,null," SI = F_2 / (1 + F_1 / SOBJECT)",-0.4679723526827208,356.551385570489]
[null,null,516.91020085281184,622.83866500851741,-0.35045447334638125,{"$f":"f_2","v":189.69519481278334},null,null,null,null,null,null,null,null,null,null,null,"Lens_thickness",null,null,null,null,null,null,null,null,null,null,"Worksheets(\"FIND_F\").Cells(KM + 1, 39).Value = 1 / (H2 + F_2 / (1 + F_1 / (H1 + Worksheets(\"FIND_F\").Cells(KM + 1, 3).Value)))",null,null,null,null,null,null,null,null,null,null,null,null,3.4955001488853723E-3,2.0580069112925534E-3,2.3083034750585769E-3,3.6431232378036117E-3,null,null,378.79923961375709,382.07077521750779,286.08209337907624,313.95612506482303,14,null," Else",-0.50350770821245772,382.07077521750779]
[null,null,546.73194320970481,655.70258670064629,null,null,null,null,null,null,null,null,null,null,null,null,null,"f left",null,null,null,null,-178.9151158024396,"Nlysh = -178,92",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.7643847757227082E-3,1.7771534139254658E-3,1.9914487311748393E-3,3.9233634868654273E-3,null,null,407.82329321271169,411.09482881646238,265.64765813771368,293.52168982346046,15,null," SI = 100000",-0.53856098030005928,411.09482881646238]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1/0.0059","v":169.49152542372883},"f right",null,null,null,null,-13.441872241248605,"llysh = -13,44",null,null,null,null,"vh",null,null,null,null,null,null,null,null,null,null,null,null,4.0332694025600451E-3,1.4920819644209946E-3,1.670293022154319E-3,4.2036037359272438E-3,null,null,441.12720154989961,444.3987371536503,247.93781426186607,275.81184594761288,16,null," End If",-0.57314191298613781,444.3987371536503]
[null,null,{"$f":"-A18","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-4027.031583504719,"mlysh = -4027,03",null,null,null,{"$f":"XB-RB+AC18","v":-27.87403168574679},{"$f":"(n_2-n_3)/(-n_2*RA)*f_1*dkorf","v":14.768292409027477},"h left its position to the right of left end",null,null,null,null,null,null,null,null,null,null,null,4.3021540293973811E-3,1.2026968239275731E-3,1.3448363479970169E-3,4.4838439849890603E-3,null,null,479.73297049732417,483.00450610107487,232.44170087049946,260.31573255624625,17,null,"  bbii = SI + H2",-0.6072599894687376,483.00450610107487]
[null,null,{"$f":"-A19","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"f_1","v":-158.0793290106528},{"$f":"XA+RA+AC19","v":-3.2715356037506851},{"$f":"-(n_2-n_1)/(n_2*RB)*f_2*dkorf","v":-32.271535603750685},"h right uts position to the left of right end",null,null,null,null,null,null,null,null,null,null,null,4.5710386562347171E-3,9.0889933407081215E-4,1.0150787087029346E-3,4.7640842340508768E-3,null,null,525.01614630212134,528.28768190587198,218.76865964282302,246.64269132856981,18,null,null,-0.6409244407735738,528.28768190587198]
[null,null,0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"h_2","v":-3.2715356037506851},{"$f":"AA20*Z20","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,4.839923283072054E-3,6.1058780481128532E-4,6.8102010427206999E-4,5.0443244831126933E-3,null,null,578.87316243627401,582.14469804002465,206.61484521822175,234.48887690396853,19,null,null,-0.67414425408072498,582.14469804002465]
[null,null,0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AA20*AA19","v":517.16215307536925},{"$f":"AA21+Z21","v":517.16215307536925},null,null,null,null,null,null,null,null,null,null,null,null,null,5.10880790990939E-3,3.0765739709327344E-4,3.4266053470442522E-4,5.3245647321745089E-3,null,null,643.99368177918893,647.26521738293957,195.7403796804206,223.61441136616739,20,null,null,-0.70692818072355257,647.26521738293957]
[null,null,0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AB21+AB20","v":517.16215307536925},null,null,null,null,null,null,null,null,null,null,null,{"$f":"1/(ABS(f_1)+ABS(h_1))","v":5.3776925367467259E-3},null,5.3776925367467268E-3,-1.3769331108452188E-18,-2.1684043449710089E-18,5.6048049812363254E-3,null,null,724.32376369738859,727.59529930113922,185.95336069639956,213.82739238214634,21,null,null,-0.73928474387480647,727.59529930113922]
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[null,null,0,null,null,null,null,null,187.8738224916774,372.70985343981329,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,{"$f":"1/(f_2+h_2)","v":5.3641260140630679E-3},null,null,null,null,null,null,null,958.42183496366181,961.69337056741244,169.04850972399962,196.9225414097464,23,null,null,-0.8027487756301569,961.69337056741244]
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["NUMTERMS= 4",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(BK36<rmaxv,max2v,IF(BK36>rminv,max2v,BL36))","v":17.004727248890575},{"$f":"IF(BK36<rmaxv,maxy2,IF(BK36>rminv,miny2,BM36))","v":-0.73484730872965343},{"$f":"IF(OR(BM36=maxy2,BM36=miny2),1+SUM(BJ$2:BJ35),0)","v":0},36,17.004727248890575,-0.73484730872965343]
["TERMS = 2",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(BK37<rmaxv,max2v,IF(BK37>rminv,max2v,BL37))","v":17.018996490501657},{"$f":"IF(BK37<rmaxv,maxy2,IF(BK37>rminv,miny2,BM37))","v":-1.463794234570823},{"$f":"IF(OR(BM37=maxy2,BM37=miny2),1+SUM(BJ$2:BJ36),0)","v":0},37,17.018996490501657,-1.463794234570823]
["no of data = 163",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.9066286283694317,null,null,{"$f":"IF(BK38<rmaxv,max2v,IF(BK38>rminv,max2v,BL38))","v":17.04305471363412},{"$f":"IF(BK38<rmaxv,maxy2,IF(BK38>rminv,miny2,BM38))","v":-2.1809963061827826},{"$f":"IF(OR(BM38=maxy2,BM38=miny2),1+SUM(BJ$2:BJ37),0)","v":0},38,17.04305471363412,-2.1809963061827826]
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["Number of points: 81","Slope for X1 = 2,1155E-01                     Slope for X2 = 2,2387E-01                     Slope for X3 = -6,4488E-02                     Slope for X4 = 5,4283E-03                     ",null,null,null,null,null,null,null,null,null,null,null,null,16.999999999999972,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.76552013431046906,null,null,{"$f":"IF(BK40<rmaxv,max2v,IF(BK40>rminv,max2v,BL40))","v":17.122023210288695},{"$f":"IF(BK40<rmaxv,maxy2,IF(BK40>rminv,miny2,BM40))","v":-3.5574030800037049},{"$f":"IF(OR(BM40=maxy2,BM40=miny2),1+SUM(BJ$2:BJ39),0)","v":0},40,{"$f":"AD115","v":17.122023210288695},{"$f":"AP115","v":-3.5574030800037049}]
["R^2 = 0,22985",null,null,null,null,null,null,null,null,null,null,null,null,null,-0.60030586543404507,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.68584757830005283,null,null,{"$f":"IF(BK41<rmaxv,max2v,IF(BK41>rminv,max2v,BL41))","v":17.177683652860871},{"$f":"IF(BK41<rmaxv,maxy2,IF(BK41>rminv,miny2,BM41))","v":-4.2057025504512531},{"$f":"IF(OR(BM41=maxy2,BM41=miny2),1+SUM(BJ$2:BJ40),0)","v":0},41,17.177683652860871,-4.2057025504512531,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  91"]
["Adjusted R^2adj = 0,17918",null,null,null,null,null,null,null,null,null,null,null,null,null,-24.503908582705954,null,null,{"$f":"B_0","v":{"$error":"#NAME?"}},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.59978483270731009,null,null,{"$f":"IF(BK42<rmaxv,max2v,IF(BK42>rminv,max2v,BL42))","v":17.244425285639693},{"$f":"IF(BK42<rmaxv,maxy2,IF(BK42>rminv,miny2,BM42))","v":-4.820561209743234},{"$f":"IF(OR(BM42=maxy2,BM42=miny2),1+SUM(BJ$2:BJ41),0)","v":0},42,17.244425285639693,-4.820561209743234,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  92"]
["Intercept = 1,5973E+01",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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.50733189753224084,null,null,{"$f":"IF(BK43<rmaxv,max2v,IF(BK43>rminv,max2v,BL43))","v":17.322139165547483},{"$f":"IF(BK43<rmaxv,maxy2,IF(BK43>rminv,miny2,BM43))","v":-5.3972638042458847},{"$f":"IF(OR(BM43=maxy2,BM43=miny2),1+SUM(BJ$2:BJ42),0)","v":0},43,17.322139165547483,-5.3972638042458847,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  93"]
["B(0) =1,4213E+03",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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.40852154297783139,null,null,{"$f":"IF(BK44<rmaxv,max2v,IF(BK44>rminv,max2v,BL44))","v":17.41029988685203},{"$f":"IF(BK44<rmaxv,maxy2,IF(BK44>rminv,miny2,BM44))","v":-5.9315024217784007},{"$f":"IF(OR(BM44=maxy2,BM44=miny2),1+SUM(BJ$2:BJ43),0)","v":0},44,17.41029988685203,-5.9315024217784007,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  94"]
["Regression SS = 3,4904E+02",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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.30330461373960244,null,null,{"$f":"IF(BK45<rmaxv,max2v,IF(BK45>rminv,max2v,BL45))","v":17.507843545289688},{"$f":"IF(BK45<rmaxv,maxy2,IF(BK45>rminv,miny2,BM45))","v":-6.4194467797095474},{"$f":"IF(OR(BM45=maxy2,BM45=miny2),1+SUM(BJ$2:BJ44),0)","v":0},45,17.507843545289688,-6.4194467797095474,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  95"]
["Regression df = 4,E+00",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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.19142714074441008,null,null,{"$f":"IF(BK46<rmaxv,max2v,IF(BK46>rminv,max2v,BL46))","v":17.613058335535563},{"$f":"IF(BK46<rmaxv,maxy2,IF(BK46>rminv,miny2,BM46))","v":-6.8578218448909709},{"$f":"IF(OR(BM46=maxy2,BM46=miny2),1+SUM(BJ$2:BJ45),0)","v":0},46,17.613058335535563,-6.8578218448909709,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  96"]
["Residual SS = 2,7157E+02",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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.2618769817617515E-2,null,null,{"$f":"IF(BK47<rmaxv,max2v,IF(BK47>rminv,max2v,BL47))","v":17.723496669473619},{"$f":"IF(BK47<rmaxv,maxy2,IF(BK47>rminv,miny2,BM47))","v":-7.2439938153904073},{"$f":"IF(OR(BM47=maxy2,BM47=miny2),1+SUM(BJ$2:BJ46),0)","v":0},47,17.723496669473619,-7.2439938153904073,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  97"]
["Residual df = 7,6E+01",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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-5.2547020488515145E-2,null,null,{"$f":"IF(BK48<rmaxv,max2v,IF(BK48>rminv,max2v,BL48))","v":17.835918543223386},{"$f":"IF(BK48<rmaxv,maxy2,IF(BK48>rminv,miny2,BM48))","v":-7.5760643807150458},{"$f":"IF(OR(BM48=maxy2,BM48=miny2),1+SUM(BJ$2:BJ47),0)","v":0},48,17.835918543223386,-7.5760643807150458,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  98"]
["Total SS = 3,5262E+02",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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.18160427239926977,null,null,{"$f":"IF(BK49<rmaxv,max2v,IF(BK49>rminv,max2v,BL49))","v":17.946276768883052},{"$f":"IF(BK49<rmaxv,maxy2,IF(BK49>rminv,miny2,BM49))","v":-7.8529713735141655},{"$f":"IF(OR(BM49=maxy2,BM49=miny2),1+SUM(BJ$2:BJ48),0)","v":0},49,17.946276768883052,-7.8529713735141655,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  99"]
["Total df = 5,E+00",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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.31018635636672315,null,null,{"$f":"IF(BK50<rmaxv,max2v,IF(BK50>rminv,max2v,BL50))","v":18.04975527055489},{"$f":"IF(BK50<rmaxv,maxy2,IF(BK50>rminv,miny2,BM50))","v":-8.0745913781714354},{"$f":"IF(OR(BM50=maxy2,BM50=miny2),1+SUM(BJ$2:BJ49),0)","v":0},50,18.04975527055489,-8.0745913781714354,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,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,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,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,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,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,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,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,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,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,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,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,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,"miki  100"]
["S^2 = 3,5733E+00",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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.43363171101607573,null,null,{"$f":"IF(BK51<rmaxv,max2v,IF(BK51>rminv,max2v,BL51))","v":18.140871320849321},{"$f":"IF(BK51<rmaxv,maxy2,IF(BK51>rminv,miny2,BM51))","v":-8.2418366584481966},{"$f":"IF(OR(BM51=maxy2,BM51=miny2),1+SUM(BJ$2:BJ50),0)","v":0},51,18.140871320849321,-8.2418366584481966,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,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,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,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,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,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,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,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,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,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,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,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,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":"RM52-$VK$52","v":18.52700075231192},18.371339972261922,18.213011900270828,18.052070043705555,null,17.888568588995639,17.72256239707059,17.554106998398368,17.38325858760777,17.210074017676959,17.034610793669202,16.856927065998548,16.677081623205936,16.495133884227414,16.311143890135213,16.125172295333186,15.937280358186797,15.747529931068811,15.555983449801175,15.362703922474594,15.167754917625359,14.971200551751451,14.773105476148942,14.573534863048792,14.372554391037511,14.170230229742003,13.966629023761413,13.761817875828854,13.555864329186306,13.348836349155846,13.140802303892883,12.931830944305375,12.721991383126351,12.511353073125974,12.299985784451167,12.087959581082714,11.875344796399077,11.662212007839628,11.448632010659139,11.234675790769302,11.02041449666217,10.805919410413878,10.591261917768236,10.376513477301216,10.161745588670044,9.9470297599521018,9.7324374740817632,9.518040154394356,9.3039091292904175,9.0901155960341384,8.8767305837042159,8.6638249153159279,8.451469169138079,8.2397336392296552,8.0286882952241854,7.8184027413935837,7.608946175024812,7.4003873441462247,7.1927945046444677,6.986235376813454,6.780777101382597,6.5764861950720501,6.3734285057279294,6.1716691670911246,5.971272553258359,{"$f":"TZ52-$VK$52","v":5.7723022328951856},5.5748209232642694,5.3788904441352372,5.1845716716434822,4.9919244921695167,4.8010077563111508,4.6118792330240694,4.424595564007177,4.2392122184119216,4.055783447955605,3.874362242519652,3.6950002863167128,3.5177479147084796,3.3426540717591422,3.1697662686082708,2.9991305427481052,2.8307914182880154,2.6647918672910009,2.5011732722638271,2.3399753898823974,2.1812363160327664,2.0249924522456411,1.8712784736000572,1.7201272981708087,1.5715700580895771,1.4256360722889099,1.2823528209926849,1.1417459220148771,1.0038391089236427,0.86865421112446484,0.73621113591090648,0.60652785252744934,0.4796203782846078,0.35550276676067938,0.23418709812028737,0.11568347157430026,{"$f":"VJ52-$VK$52","v":0}]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"T88","v":-439.97142857142859},{"$f":"U88","v":-66.75},null,null,null,null,null,{"$f":"-(x_3-XB)/y_3","v":8.9187514742247398},{"$f":"-1/AA89","v":-0.11212331713581297},{"$f":"-1/SQRT(1+AB89^2)","v":-0.99377283400827321},{"$f":"AB89*AC89","v":0.11142510662846523},{"$f":"x_3-x_2","v":-69.412954975081433},{"$f":"y_3-y_2","v":-2.1278046339631373},{"$f":"AE89*AD89-AF89*AC89","v":-9.8489003508047883},{"$f":"ASIN(AG89/SQRT(AE89^2+AF89^2))","v":-0.14230166230230876},{"$f":"IF(ABS(SIN(AH89)*dEIKTHS/DEIKTHS_2)>1,\"\",ASIN(SIN(AH89)*dEIKTHS/1))","v":-0.26253968994920462},{"$f":"ATAN(AD89/AC89)","v":-0.11165697182148412},{"$f":"IF(AI89=\"\",\"\",ABS(AI89)-ABS(AJ89))","v":0.1508827181277205},{"$f":"IF(AK89=\"\",\"\",x_3-y_3/TAN(AK89))","v":-181.43218135124391},null,"H1",{"$f":"IF(AK89=\"\",\"\",x_3+(y_2-y_3)/TAN(AK89))","v":-27.457739730720249},null,{"$f":"AL89","v":-181.43218135124391},null,null,null,{"$f":"IF(vsteps<1,1000,IF(vsteps<5,IF(x_4=\"\",x_3,x_4),1000))","v":1000},{"$f":"IF(vsteps<1,1000,IF(vsteps<5,x_3,1000))","v":1000},{"$f":"IF(vsteps<1,1000,IF(vsteps<5,x_2,1000))","v":1000},{"$f":"IF(vsteps<1,1000,IF(vsteps<5,X_1,1000))","v":1000},{"$f":"IF(vsteps<2,1000,IF(vsteps<5,x_4,1000))","v":1000},{"$f":"IF(vsteps<2,1000,IF(vsteps<5,40,1000))","v":1000},{"$f":"IF(vsteps<3,1000,IF(vsteps<5,IF(AY89=\"\",x_3,h_1-1000*ABS(h_1)),1000))","v":1000},{"$f":"IF(vsteps<3,1000,IF(vsteps<=5,X_1,1000))","v":1000},null,null,"vsteps",12,null,20,{"$f":"IF(vsteps>6,1000,KL_Y_THICK*60/160)","v":1000},20,1000,{"$f":"IF(vsteps<4,\"\",\"4  From the intersection Draw the line PARALLEL TO THE y- AXIS\")","v":"4  From the intersection Draw the line PARALLEL TO THE y- AXIS"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"on left",null,"dy/dx","KATH3","KATH3X","KATH3Y","DX3","DY_3","exoteriko","prospo","diathl","DF","klisi","taf_2","T²X2-y2T+Xa","diakrinoysa","XLYSHxl_3","YLYSHyl_3",{"$f":"0","v":0},{"$f":"y_3","v":21.282195366036863},{"$f":"y_2","v":23.41},{"$f":"AS90","v":23.41},{"$f":"IF(vsteps<1,1000,IF(vsteps<5,IF(x_4=\"\",y_3,0),1000))","v":1000},{"$f":"IF(vsteps<1,1000,IF(vsteps<5,y_3,1000))","v":1000},{"$f":"IF(vsteps<1,1000,IF(vsteps<5,y_2,1000))","v":1000},{"$f":"AW90","v":1000},{"$f":"IF(vsteps<2,1000,IF(vsteps<5,IF(AY89=\"\",\"\",0),1000))","v":1000},{"$f":"IF(vsteps<2,1000,IF(vsteps<5,IF(AY89=\"\",\"\",(y_2/(H_1_par-AY89)*(2*20-AY89))),1000))","v":1000},{"$f":"IF(vsteps<3,1000,IF(vsteps<5,y_2,1000))","v":1000},{"$f":"BA90","v":1000},null,null,"To find the H1",null,null,{"$f":"BH89","v":20},25,20,25,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(vsteps>3,H_1_par,1000)","v":-27.457739730720249},{"$f":"IF(vsteps>3,150,1000)","v":150}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"FROM LEFT","Y1",{"$f":"Y87","v":23.41},{"$f":"Y91","v":23.41},{"$f":"-(Xl_2-XB)/YL_1","v":8.0973918309345354},{"$f":"-1/AA91","v":-0.12349655554269851},{"$f":"1/SQRT(1+AB91^2)","v":0.99246043330982969},{"$f":"AB91*AC91","v":-0.12256544502617801},{"$f":"Xl_2-XL_1","v":108.79773314304828},{"$f":"0","v":0},{"$f":"AE91*(-AD91)-0*AD91*(-1)","v":13.334842580517069},{"$f":"ASIN(AG91/AE91)","v":0.12287440711898535},{"$f":"ASIN(SIN(AH91)/dEIKTHS)","v":6.7025826905735705E-2},{"$f":"ATAN(AD91/AC91)","v":-0.12287440711898535},{"$f":"-(ABS(AJ91)-ABS(AI91))","v":-5.5848580213249649E-2},{"$f":"TAN(AK91)","v":-5.5906717845346669E-2},{"$f":"TAF_2^2*Xl_2-YL_1*TAF_2+XA","v":-233.8200039377702},{"$f":"AM91^2-(TAF_2^2+1)*AN92","v":68741.146806996359},{"$f":"(AM91+SQRT(AN91))/(TAF_2^2+1)","v":28.276943868792443},{"$f":"SQRT(RA^2-(XL_3-XA)^2)","v":19.525645369838958},null,null,null,{"$f":"h_2","v":-3.2715356037506851},null,"FROM LEFT",null,null,null,"TO H2",null,"PARALLEL LINE",null,null,null,null,null,25,{"$f":"IF(vsteps<9,KL_Y_THICK/160*125,1000)","v":1000},25,1000,{"$f":"IF(vsteps<5,\"\",\"5 draw the parallel ray from left, it cut the x-axis at RIGHT FOCAL POINT = \"&TEXT(XL_F,\"0,00\")&\"FROM PARAXIAL F RIGHT = \"&TEXT(F_RIGHT,\"0,00\"))","v":"5 draw the parallel ray from left, it cut the x-axis at RIGHT FOCAL POINT = 183,94FROM PARAXIAL F RIGHT = 186,42"},null,null,null,null,null,null,null,null,null,{"$f":"BV90","v":-27.457739730720249},{"$f":"IF(vsteps>3,-150,1000)","v":-150}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x1",-150,{"$f":"XB-SQRT(RB^2-(YL_1)^2)","v":-41.202266856951724},"dy/dx","KATH4","KATH4X","KATH4Y","DX4","DY4","exoteriko","prospo","diathl","DF",null,"focus from left",null,{"$f":"YL_1^2+(TAF_2*Xl_2)^2-2*YL_1*TAF_2*Xl_2+XA^2-RA^2","v":-14025.514961562811},{"$f":"SQRT(AN91)","v":262.18532912235258},null,null,"y_2^2+taf^2*x_2^2-2*y_2*taf*x_2+XB^2-RB^2",null,null,null,{"$f":"IF(vsteps<5,1000,IF(vsteps<9,XL_1,1000))","v":1000},{"$f":"IF(vsteps<5,1000,IF(vsteps<9,Xl_2,1000))","v":1000},{"$f":"IF(vsteps<5,1000,IF(vsteps<9,XL_3,1000))","v":1000},{"$f":"IF(vsteps<5,1000,IF(vsteps<9,XL_F,1000))","v":1000},{"$f":"IF(vsteps<=5,1000,IF(vsteps<9,XL_F,1000))","v":1000},{"$f":"IF(vsteps<=5,1000,IF(vsteps<9,0,1000))","v":1000},{"$f":"IF(vsteps<7,1000,IF(vsteps<9,2*hl_2,1000))","v":1000},{"$f":"IF(vsteps<7,1000,IF(vsteps<9,XL_1,1000))","v":1000},null,null,"LINE H2",null,{"$f":"-135*KL_THICK_MODEL/270","v":-265.5},{"$f":"BI91-dy","v":944.375},-265.5,944.375,{"$f":"IF(vsteps<6,\"\",\"6  Draw the line from RIGHT focal point SO THAT IT CAN meet the continuation of the  incoming parallel ray\"\"\")","v":"6  Draw the line from RIGHT focal point SO THAT IT CAN meet the continuation of the  incoming parallel ray\""},null,null,null,null,null,null,null,null,null,{"$f":"IF(vsteps>7,hl_2,1000)","v":-2.6897510028270624},{"$f":"IF(vsteps>7,150,1000)","v":150}]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"dEIKTHS","v":1.83},null,null,null,null,{"$f":"SQRT(AC91^2+AD91^2)","v":1},{"$f":"SQRT(AC93^2+AD93^2)","v":1},null,null,null,null,{"$f":"SIN(AH93)","v":0.12951213456521304},{"$f":"AH94*dEIKTHS/DEIKTHS_2","v":0.19750600521194991},null,{"$f":"-AF94","v":0},{"$f":"AL93-XL_3","v":155.66156026134649},{"$f":"XL_3","v":28.276943868792443},{"$f":"AN93/AK93","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"-210*KL_THICK_MODEL/270","v":-413},{"$f":"BI93-dy","v":833.125},-413,833.125,{"$f":"IF(vsteps<8,\"\",\"8  From the intersection Draw the line PARALLEL TO THE y- AXIS\")","v":"8  From the intersection Draw the line PARALLEL TO THE y- AXIS"}]
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[]
[null,{"$f":"IF(AND( vsteps>=9,vsteps<=10),KL_THICK_MODEL/270*110,1000)","v":1000},{"$f":"\"we find the RAY  that starts from  x = \" &  TEXT(xxx,\"0\")  & \" y = \" & TEXT(yyy, \"0,00\") & \"for which the refracted comes out parallel to the incident\"","v":"we find the RAY  that starts from  x = -200 y = 15,00for which the refracted comes out parallel to the incident"}]
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[null,{"$f":"IF(AND( vsteps>=9,vsteps<=10),KL_THICK_MODEL/270*110,1000)","v":1000},{"$f":"\"we find that the extension of the incident  RAY cuts the x-axis at x = \" & TEXT(E452, \"0,00\") & \"the paraxial theory = \"& TEXT(nodal_1,\"0,00\") & \" the extensicion backswrds of the refracted cuts at x = \" & TEXT(H452,\"0,00\") & \"value from paraxial R[-3]C[-2]theory  = \"& TEXT(nodal_2,\"0,00\")","v":"we find that the extension of the incident  RAY cuts the x-axis at x = 1000,00the paraxial theory = 3,74 the extensicion backswrds of the refracted cuts at x = 1000,00value from paraxial R[-3]C[-2]theory  = 28,34"}]
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[{"$f":"IF(OR(vsteps<=8,vsteps>12),900,xxx)","v":-200},{"$f":"IF(OR(vsteps<=8,vsteps>12),900,B470)","v":-42.61188831783295},{"$f":"IF(OR(vsteps<=8,vsteps>12),900,D470)","v":29.059323477145295},{"$f":"IF(OR(vsteps<=8,vsteps>12),900,400)","v":400},{"$f":"IF(OR(vsteps<=8,vsteps>12),900,B479)","v":-42.61188831783295},{"$f":"IF(OR(vsteps<=8,vsteps>12),900,-B480/TAN(A470)+B479)","v":3.6881127617392337},"1ST NODAL [POINT"]
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