Question

A ray `PQ` incident on face `AB` of a prism `ABC`, as shown in Fig., emerges from the face `AC` such that `AQ = AR`. Draw the ray diagram showing the pasage of the ray through the prism. If the angle of prism is `60^@` and refractive index of the material of the prism is `sqrt(3) ,` determine the values of angle of incidence and angle of deviation.
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Answer 1

As the refracted ray passes such that `AQ = AR`, it must go parallel to the base of the prism suffring minimum deviation.
`r = A//2 = (60)/(2) = 30^(@)`
`mu = (sin i)/(sin r)/(sin i)/(sin 30^(@))`
`:. sin I = mu sin 30^(@) = sqrt(3) xx (1)/(2)`
`i = 60^(@)`
As `i + e =A + delta_(m)`
`2i = 60^(@) + delta_(m), delta_(m) = 2 i - 60^(@) = 120^(@) - 60^(@)`
`delta_(m) = 60^(@)`