A light ray is incident on the surface of a sphere of refractive index n at an angle of incidence θ 0 𝜃 0 . The ray partially refracts into the sphere with angle of refraction ϕ 0 𝜙 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 α 𝛼 . Match the quantities mentioned in List-I with their values in List-II and choose the correct option. List-I List-II (P) If n = 2 and α = 180 ∘ 𝛼 = 180 ∘ , then all the possible values of θ 0 𝜃 0 will be (1) 30 ∘ 30 ∘ and 0 ∘ 0 ∘ (Q) If n = √ 3 𝑛 = 3 and α = 180 ∘ 𝛼 = 180 ∘ , then all the possible values of θ 0 𝜃 0 will be (2) 60 ∘ 60 ∘ and 0 ∘ 0 ∘ (R) If n = √ 3 𝑛 = 3 and α = 180 ∘ 𝛼 = 180 ∘ , then all the possible values of ϕ 0 𝜙 0 will be (3) 45 ∘ 45 ∘ and 0 ∘ 0 ∘ (S) If n = √ 2 𝑛 = 2 and θ 0 = 45 ∘ 𝜃 0 = 45 ∘ , then all the possible values of α 𝛼 will be (4) 150 ∘ 150 ∘ (5) 0 ∘ 0 ∘ (A) P → 5; Q → 2; R → 1; S → 4 (B) P → 5; Q → 1; R → 2; S → 4 (C) P → 3; Q → 2; R → 1; S → 4 (D) P → 3; Q → 1; R → 2; S → 5
A light ray is incident on the surface of a sphere of refractive index n at an angle of incidence θ 0 𝜃 0 . The ray partially refracts into the sphere with angle of refraction ϕ 0 𝜙 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 α 𝛼 . Match the quantities mentioned in List-I with their values in List-II and choose the correct option. List-I List-II (P) If n = 2 and α = 180 ∘ 𝛼 = 180 ∘ , then all the possible values of θ 0 𝜃 0 will be (1) 30 ∘ 30 ∘ and 0 ∘ 0 ∘ (Q) If n = √ 3 𝑛 = 3 and α = 180 ∘ 𝛼 = 180 ∘ , then all the possible values of θ 0 𝜃 0 will be (2) 60 ∘ 60 ∘ and 0 ∘ 0 ∘ (R) If n = √ 3 𝑛 = 3 and α = 180 ∘ 𝛼 = 180 ∘ , then all the possible values of ϕ 0 𝜙 0 will be (3) 45 ∘ 45 ∘ and 0 ∘ 0 ∘ (S) If n = √ 2 𝑛 = 2 and θ 0 = 45 ∘ 𝜃 0 = 45 ∘ , then all the possible values of α 𝛼 will be (4) 150 ∘ 150 ∘ (5) 0 ∘ 0 ∘ (A) P → 5; Q → 2; R → 1; S → 4 (B) P → 5; Q → 1; R → 2; S → 4 (C) P → 3; Q → 2; R → 1; S → 4 (D) P → 3; Q → 1; R → 2; S → 5