Question

A ray of light passing through a prism (µ = `sqrt3`) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction with in the prism. Then. the angle of prism is ______ (in degrees).

Options

• 50

• 60

• 70

• 80

Answer 1

A ray of light passing through a prism (µ = `sqrt3`) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction with in the prism. Then. the angle of prism is 60 (in degrees).

Explanation:

Given i = 2r₁ = A

And at minimum deviation r₁ = r₂ = `"A"/2`

From Snell's law,

µ₁ sin i = µ₂ sin r₁

∴ 1.sin i = `sqrt3` sin r₁ 

⇒ 1 sin A = `sqrt3  "sin" "A"/2`

⇒ 2 sin`"A"/2  "cos" "A"/2=sqrt3  "sin" "A"/2`

⇒ cos`"A"/2=sqrt3/2`

⇒ `"A"/2` = 30° or, A = 60°

Hence angle of prism = 60°