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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.
Solution
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, δm = 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.
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