A light ray is incident on the surface of a sphere of refractive index n at an angle of incidence 0. The ray partially refracts into the sphere with angle of refraction 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 . Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
- P → 5; Q → 2; R → 1; S → 4
- P → 5; Q → 1; R → 2; S → 4
- P → 3; Q → 2; R → 1; S → 4
- P → 3; Q → 1; R → 2; S → 5
Answer
(1) P → 5; Q → 2; R → 1; S → 4
Solution
Deviation with one internal reflection: =( 0- 0)+(180 -2 0)+( 0- 0)=180 +2 0-4 0.
=180 ⇒ 0=2 0; with 0=n 0: 2 0 0=n 0 ⇒ 0=0 or 0= n2.
(P) n=2: 0=1 ⇒ only 0=0, 0=0 → 5.
(Q), (R) n= 3: 0= 32 ⇒ 0=30 , 0=60 ; also 0 . Q → 2, R → 1.
(S) n= 2, 0=45 : 0= 12, 0=30 ; =180 +90 -120 =150 → 4.
Answer: (A)