A ray of light is incident at an angle of 60∘ on one face of a prism which has refracting angle of 30∘. The ray emerging out of the prism makes an angle of 30∘ with the incident ray. If the refractive index of the material of the prism is μ=√a, find the value of a.
For a prism with refracting angle A, and angle of deviation of light δ, We have
i+e=δ+A
60∘+e=30∘+30∘
Hence e=0∘
Applying Snell's law at the point of emergence,
μsinr2=sine=0
r2=0
Also we know that for a prism, r1+r2=A
Then r1=A=30∘
Applying Snell's Law at the point of incidence,
sini=μsinr1
Hence, μ=√3=√a
Hence a=3