Question

For a glass prism `(µ = sqrt(3))` the angle of minimum deviation is equal to the angle of the prism. Find the angle of the prism.

Answer 1

The refractive index of prism angle A and angle of minimum deviation `δ_m` is given by

`mu = (sin[((A  +  δ_m))/2])/(sin(A/2))`

Here we are given, δ_m = A

Substituting the value, we have `mu = (sin  A)/(sin  A/2)`

⇒ `mu = (2sin  A/2 cos  A/2)/(sin  A/2) = 2 cos  A/2`

⇒ `mu = (sin  A)/(sin  A/2) = (2sin  A/2 cos   A/2)/(sin  A/2) = 2 cos  A/2`

For the given value of refractive index,

We have, `cos  A/2 = sqrt(3)/2 ⇒ A/2` = 30°

or A = 60°

This is the required value of prism angle.