A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is

Question

A prism ABC of angle 30° has its face AC silvered. A ray of light incident at an angle of 45° at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is (A) 1.5 (B) (3/√2) (C) √2 (D) (4/3)

Tardigrade Admin · Accepted Answer

A = r + 0 ⇒ r = 30° <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/6b64fc3b4968f24197fa41953f98cb60-.png" /> μ = ( sin i/ sin r) =( sin 45°/ sin 30°) = √2

Q. A prism $A BC$ of angle $3 0^{\circ}$ has its face $A C$ silvered. A ray of light incident at an angle of $4 5^{\circ}$ at the face $A B$ retraces its path after refraction at face $A B$ and reflection at face $A C$ . The refractive index of the material of the prism is

$1.5$

$\frac{3}{2}$

$2$

$\frac{4}{3}$

$A = r + 0 \Rightarrow r = 3 0^{\circ}$

$μ = \frac{s i n i}{s i n r} = \frac{s i n 4 5 ^{\circ}}{s i n 3 0 ^{\circ}} = 2$

Q. A prism ABC of angle 30∘ has its face AC silvered. A ray of light incident at an angle of 45∘ at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is

1.5

2​3​

2​

34​

A=r+0⇒r=30∘ μ=sinrsini​=sin30∘sin45∘​=2​

Q. A prism $A BC$ of angle $3 0^{\circ}$ has its face $A C$ silvered. A ray of light incident at an angle of $4 5^{\circ}$ at the face $A B$ retraces its path after refraction at face $A B$ and reflection at face $A C$ . The refractive index of the material of the prism is

$1.5$

$\frac{3}{2}$

$2$

$\frac{4}{3}$

$A = r + 0 \Rightarrow r = 3 0^{\circ}$

$μ = \frac{s i n i}{s i n r} = \frac{s i n 4 5 ^{\circ}}{s i n 3 0 ^{\circ}} = 2$