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// Scilab Code Ex4.10: Page-197
clc;clear;
w1 = 0.02;....// Magnitude of the dispersive power of first lens
w2 = 0.04;....// Magnitude of the dispersive power of second lens
// Let 1/f1 = x and 1/f2 = y, then
// The condition for achromatic combination of two lenses, w1/f1 + w2/f2 = 0 => w1*x + w2*y = 0 --- (I)
F = 20;....// Given focal length of achromatic doublet, cm
// Also F = 1/f1 + 1/f2 => F = x + y ---- (II)
A = [w1 w2; 1 1]; // Square matrix
B = [0;1/F]; // Column vector
X = inv(A)*B; // Characteristic roots of the simultaneous equations, cm
f1 = 1/X(1); // Focal length of convex lens, cm
f2 = 1/X(2); // Focal length of concave lens, cm
printf("\nThe focal length of convex lens = %2d cm", ceil(f1));
printf("\nThe focal length of concave lens = %2d cm", ceil(f2));
// Result
// The focal length of convex lens = 10 cm
// The focal length of concave lens = -20 cm
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