A ray of light is incident at 60° on one face of a prism of angle 30° and the emergent ray makes 30° with the incident ray. The refractive index of the prism is

Question

A ray of light is incident at 60° on one face of a prism of angle 30° and the emergent ray makes 30° with the incident ray. The refractive index of the prism is (A) 1.732  (B) 1.414 (C) 1.5  (D) 1.33

Tardigrade Admin · Accepted Answer

Here, i = 60°, A = 30°, δ= 30° As i+ e = A + δ e = A + δ - i = 30° + 30° - 60° = 0° Hence emergent ray is normal to the surface.

e= 0° ⇒ r2 = 0° As r1 +r2 = A ∴ r1 = A -r2 = 30° - 0° = 30° μ =( sin i/sin r1) = (sin 60°/sin 30°) = (√3/2)× (2/1) = √3 = 1.732

Q. A ray of light is incident at $6 0^{\circ}$ on one face of a prism of angle $3 0^{\circ}$ and the emergent ray makes $3 0^{\circ}$ with the incident ray. The refractive index of the prism is

$1.732$

$1.414$

$1.5$

$1.33$

1.6

Q. A ray of light is incident at 60∘ on one face of a prism of angle 30∘ and the emergent ray makes 30∘ with the incident ray. The refractive index of the prism is

1.732

1.414

1.5

1.33

1.6

Here, i=60∘,A=30∘,δ=30∘ As i+e=A+δ e=A+δ−i=30∘+30∘−60∘=0∘ Hence emergent ray is normal to the surface. e=0∘ ⇒r2​=0∘ As r1​+r2​=A ∴r1​=A−r2​=30∘−0∘=30∘ μ=sinr1​sini​=sin30∘sin60∘​ =23​​×12​=3​ =1.732

Q. A ray of light is incident at $6 0^{\circ}$ on one face of a prism of angle $3 0^{\circ}$ and the emergent ray makes $3 0^{\circ}$ with the incident ray. The refractive index of the prism is

$1.732$

$1.414$

$1.5$

$1.33$