Question

An equilateral prism is made up of material of refractive index √3. The angle of minimum deviation of light passing through the prism is_________.

Answer 1

Answer:

The answer is 60°

Explanation:

Refractive index of a prism is given by the eq uation.

Refractive index   = [Sin{A+DM}/2]/SinA/2

= Sin[{60+Dm}/2]/Sin(60/2)=√3

= Sin{30+(Dm/2)}/Sin30=√3

= Sin{30+(Dm/2)}×2=√3

= 30+(Dm/2)= Sin-1(√3/2)=60°= Dm/2 = 60°–30

Dm =30×2=60°

Answer 2

Given:

An equilateral prism.

⇒ A = 60°

The refractive index of the prism, μ = √3

To Find:

The angle of minimum deviation of light passing through the prism.

Calculation:

- We know that the refractive index can be given as:

μ = sin {(A+δ$_{m}$)/2} / sin (A/2)

⇒ √3 = sin {(60+δ$_{m}$)/2} / sin (60/2)°

⇒ sin {30° + (δ$_{m}$/2)} = √3 × sin 30°

⇒ sin {30° + (δ$_{m}$/2)} = √3/2

⇒ 30° + (δ$_{m}$/2) = sin⁻¹(√3/2)

⇒ δ$_{m}$/2 = 60° - 30°

⇒ δ$_{m}$ = 30° × 2

⇒ δ$_{m}$ = 60°

- So, the angle of minimum deviation of light passing throughh the prism is 60°.