Question

The refractive index of the material of glass is `sqrt3`. If the angle of minimum deviation is equal to the angle of the prism, then the angle of the prism is ______.

`(cos30^circ = sqrt3/2 = sin60^circ, sin30^circ = 1/2 = cos60^circ)`

Options

• 30°

• 60°

• 45°

• 50°

Answer 1

The refractive index of the material of glass is `sqrt3`. If the angle of minimum deviation is equal to the angle of the prism, then the angle of the prism is 60°.

Explanation:

Given, μ_g = `sqrt3`, δ_m = A

As we know, the refractive index of the prism,

`mu_g = (sin((A + delta_m)/2))/(sin  A/2)`

⇒ `sqrt3 = (sin((A + A)/2))/(sin  A/2)`

= `(sin A)/(sin  A/2) = (2sin  A/2cos  A/2)/(sin  A/2)` (∵ sin2θ = 2sinθ cosθ)

= `2cos  A/2`

⇒ `cos  A/2 = sqrt3/2 = cos30^circ ⇒ A/2 = 30^circ`

or A = 60°