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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.
Solution
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 Dm = 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`
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