Question

A light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence $\theta_{0}$. The ray partially refracts into the sphere with angle of refraction $\phi_{0}$ and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is $\alpha$. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

| List-I | |
|--------|--------|
| (P) | If $n=2$ and $\alpha=180^{\circ}$, then all the possible values of $\theta_{0}$ will be |
| (Q) | If $\mathrm{n}=\sqrt{3}$ and $\alpha=180^{\circ}$, then all the possible values of $\theta_{0}$ will be |
| (R) | If $\mathrm{n}=\sqrt{3}$ and $\alpha=180^{\circ}$, then all the possible values of $\phi_{0}$ will be |
| (S) | If $\mathrm{n}=\sqrt{2}$ and $\theta_{0}=45^{\circ}$, then all the possible values of $\alpha$ will be |

| List-II | |
|---------|--------|
| (1) | 30° and 0° |
| (2) | 60° and 0° |
| (3) | 45° and 0° |
| (4) | 150° |
| (5) | 0° |

Accepted Answer

(A) $\mathrm{P} \rightarrow 5 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 1 ; \mathrm{S} \rightarrow 4$

Answer

(B) $\mathrm{P} \rightarrow 5 ; \mathrm{Q} \rightarrow 1 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 4$

Answer

(C) $\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 1 ; \mathrm{S} \rightarrow 4$

Answer

(D) $\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 1 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 5$

JEE Advanced · 2024 · 26 May 2024 · Paper 1 · Geometrical Optics

Solution

More JEE Advanced questions on Geometrical Optics

List-I
(P)	If $n = 2$ and $α = 18 0^{\circ}$ , then all the possible values of $θ_{0}$ will be
(Q)	If $n = 3$ and $α = 18 0^{\circ}$ , then all the possible values of $θ_{0}$ will be
(R)	If $n = 3$ and $α = 18 0^{\circ}$ , then all the possible values of $ϕ_{0}$ will be
(S)	If $n = 2$ and $θ_{0} = 4 5^{\circ}$ , then all the possible values of $α$ will be