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["A spherical lens in the paraxial approximation.",null,null,null,null,null,null,null," "]
[null,null,"first interface drawing"]
[null,null,"x","z",null,null,"Type Ctrl+m to run the macro."]
["R1 (cm)",3,2,{"$f":"-SIGN($B$4)*SQRT($B$4^2-C4^2)+$B$4","v":0.76393202250021019}]
["R2 (cm)",-3,{"$f":"C4-0.1","v":1.9},{"$f":"-SIGN($B$4)*SQRT($B$4^2-C5^2)+$B$4","v":0.67836264675122004}]
["d",4,{"$f":"C5-0.1","v":1.7999999999999998},0.59999999999999964]
[null,null,1.6999999999999997,0.52815858113834491]
["n1",1,1.5999999999999996,0.46228449191009569]
["n2",1.5,1.4999999999999996,0.40192378864668354]
[null,null,1.3999999999999995,0.3467001677156798]
["object x",0,1.2999999999999994,0.29629883308084493]
["object z<0",-10,1.1999999999999993,0.25045458302649592]
["q(max)",0.1,1.0999999999999992,0.20894285260942702]
["limit",20,0.99999999999999922,0.17157287525380971]
[null,null,0.89999999999999925,0.1381823957491628]
[null,null,0.79999999999999927,0.10863354103980782]
[null,null,0.69999999999999929,8.2809570837035551E-2]
[null,null,0.59999999999999931,6.0612308660186187E-2]
[null,null,0.49999999999999933,4.1960108450191935E-2]
[null,null,0.39999999999999936,2.6786250536298795E-2]
[null,null,0.29999999999999938,1.5037688680139993E-2]
[null,null,0.19999999999999937,6.67409058084667E-3]
[null,null,9.9999999999999367E-2,1.6671298870098994E-3]
[null,null,-6.3837823915946501E-16,0,null,"The ray tracing matrices:"]
[null,null,-0.10000000000000064,1.6671298870098994E-3,null,"T23",null,"R2",null,"Td",null,"R1",null,"T12",null,"r1"]
[null,null,{"$f":"C25-0.1","v":-0.20000000000000065},6.674090580847114E-3,null,1,0,1,{"$f":"($B$9-$B$8)/$B$5","v":-0.16666666666666666},1,0,1,{"$f":"($B$8-$B$9)/$B$4","v":-0.16666666666666666},1,0,{"$f":"$B$8*$B$13","v":0.1}]
[null,null,-0.30000000000000066,1.5037688680139993E-2,null,{"$f":"($B$14-$B$6)/$B$9","v":10.666666666666666},1,0,1,{"$f":"$B$6/$B$9","v":2.6666666666666665},1,0,1,{"$f":"-$B$12/$B$8","v":10},1,{"$f":"$B$11","v":0}]
[null,null,-0.40000000000000069,2.6786250536298795E-2,null,"The results of the matrix multiplications:"]
[null,null,-0.50000000000000067,4.1960108450191935E-2,null,{"$f":"MMULT(F26:G27,H29:H30)","v":-0.20370370370370369},null,{"$f":"MMULT(H26:I27,J29:J30)","v":-0.20370370370370369},null,{"$f":"MMULT(J26:K27,L29:L30)","v":-6.6666666666666652E-2},null,{"$f":"MMULT(L26:M27,N29:N30)","v":-6.6666666666666652E-2},null,{"$f":"MMULT(N26:O27,P26:P27)","v":0.1}]
[null,null,-0.60000000000000064,6.0612308660186631E-2,null,-1.350617283950617,null,0.8222222222222223,null,0.8222222222222223,null,1,null,1]
[null,null,{"$f":"C30-0.1","v":-0.70000000000000062},8.2809570837035551E-2]
[null,null,{"$f":"C31-0.1","v":-0.8000000000000006},0.10863354103980782]
[null,null,{"$f":"C32-0.1","v":-0.90000000000000058},0.13818239574916324,null,"Results:"]
[null,null,{"$f":"C33-0.1","v":-1.0000000000000007},0.17157287525381015,"z",-10,0,4,20]
[null,null,{"$f":"C34-0.1","v":-1.1000000000000008},0.20894285260942791,"ray1 x",0,1,0.8222222222222223,-1.350617283950617]
[null,null,-1.2000000000000008,0.25045458302649637,"ray2 x",0,0.66666666666666674,0.54814814814814827,-0.90041152263374458]
[null,null,-1.3000000000000009,0.29629883308084537,"ray3 x",0,0.33333333333333348,0.27407407407407419,-0.45020576131687257]
[null,null,-1.400000000000001,0.34670016771568068,"ray4 x",0,1.3877787807814457E-16,1.1410625530869666E-16,-1.8743580076233352E-16]
[null,null,-1.5000000000000011,0.40192378864668488,"ray5 x",0,-0.3333333333333332,-0.27407407407407397,0.45020576131687212]
[null,null,-1.6000000000000012,0.46228449191009657,"ray6 x",0,-0.66666666666666652,-0.54814814814814805,0.90041152263374458]
[null,null,-1.7000000000000013,0.5281585811383458,"ray7 x",0,-1,-0.8222222222222223,1.350617283950617]
[null,null,-1.8000000000000014,0.60000000000000098]
[null,null,-1.9000000000000015,0.67836264675122138]
[null,null,-2.0000000000000013,0.76393202250021153]
[]
[null,null,"second interface drawing"]
[null,null,"x","z"]
[null,null,2,{"$f":"-SIGN($B$5)*SQRT($B$5^2-C48^2)+$B$5+$B$6","v":3.2360679774997898}]
[null,null,{"$f":"C48-0.1","v":1.9},{"$f":"-SIGN($B$5)*SQRT($B$5^2-C49^2)+$B$5+$B$6","v":3.32163735324878}]
[null,null,{"$f":"C49-0.1","v":1.7999999999999998},3.4000000000000004]
[null,null,1.6999999999999997,3.4718414188616551]
[null,null,1.5999999999999996,3.5377155080899043]
[null,null,1.4999999999999996,3.5980762113533165]
[null,null,1.3999999999999995,3.6532998322843202]
[null,null,1.2999999999999994,3.7037011669191551]
[null,null,1.1999999999999993,3.7495454169735041]
[null,null,1.0999999999999992,3.791057147390573]
[null,null,0.99999999999999922,3.8284271247461903]
[null,null,0.89999999999999925,3.8618176042508372]
[null,null,0.79999999999999927,3.8913664589601922]
[null,null,0.69999999999999929,3.9171904291629644]
[null,null,0.59999999999999931,3.9393876913398138]
[null,null,0.49999999999999933,3.9580398915498081]
[null,null,0.39999999999999936,3.9732137494637012]
[null,null,0.29999999999999938,3.98496231131986]
[null,null,0.19999999999999937,3.9933259094191533]
[null,null,9.9999999999999367E-2,3.9983328701129901]
[null,null,-6.3837823915946501E-16,4]
[null,null,-0.10000000000000064,3.9983328701129901]
[null,null,{"$f":"C69-0.1","v":-0.20000000000000065},3.9933259094191529]
[null,null,-0.30000000000000066,3.98496231131986]
[null,null,-0.40000000000000069,3.9732137494637012]
[null,null,-0.50000000000000067,3.9580398915498081]
[null,null,-0.60000000000000064,3.9393876913398134]
[null,null,-0.70000000000000062,3.9171904291629644]
[null,null,-0.8000000000000006,3.8913664589601922]
[null,null,-0.90000000000000058,3.8618176042508368]
[null,null,-1.0000000000000007,3.8284271247461898]
[null,null,{"$f":"C78-0.1","v":-1.1000000000000008},3.7910571473905721]
[null,null,-1.2000000000000008,3.7495454169735036]
[null,null,-1.3000000000000009,3.7037011669191546]
[null,null,-1.400000000000001,3.6532998322843193]
[null,null,-1.5000000000000011,3.5980762113533151]
[null,null,-1.6000000000000012,3.5377155080899034]
[null,null,-1.7000000000000013,3.4718414188616542]
[null,null,-1.8000000000000014,3.399999999999999]
[null,null,-1.9000000000000015,3.3216373532487786]
[null,null,-2.0000000000000013,3.2360679774997885]