Answer to Question #82811 in Optics for Raphael

Question

A certain prism is found to produce a deviation of 51°0', while it produces a deviation of 62°48' for two values of the angle of incidence namely 40°6' and 82°42' respectively. Determine the refracting angle of the prism, the angle of incidence at minimum deviation and the refractive index of the material of the prism.

Answer 1

The refracting angle of the prism

A=(i+e)-δ

A=(40°6' +82°〖42〗^' )-62°48'=60°

At minimum deviation

i=e

δ_m=2i-A

The angle of incidence at minimum deviation is

i=((δ_m+A)/2)=((51+60)/2)=55°30'

The refractive index of the material of the prism

μ=sin⁡〖(δ_m+A)/2〗/sin⁡〖A/2〗 =sin⁡〖55°30'〗/sin⁡〖(60°)/2〗 =1.648.