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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