Question

A ray of monochromatic light passes through an equilateral glass prism in such a way that the angle of incidence is equal to the angle of emergence and each of these angles is 3/4 times the angle of the prism. Determine the angle of deviation and the refractive index of the glass prism.

Answer 1

Here the angle of prism A = 60°, the angle of incidence i = angle of emergence e and under this condition angle of deviation is minimum.

∴ i = e = `3/4` A = `3/4 xx 60^circ = 45^circ` and i + e = A + D,

hence D_m = 2i - A = 2 × 45° - 60° = 30°

The refractive index of the glass prism,

n = `sin((A + D_m)/2)/(sin(A/2)) = (sin((60^circ + 30^circ)/2))/(sin(60^circ/2))`

= `(sin45^circ)/(sin30^circ) = (1/sqrt2)/(1/2) = sqrt2`