A prism of refracting angle A is made of material of refractive index 2. Assume rays are incident 'i' at angle of incidence such that 0 ≤ i ≤ 9 0 ∘ . List - I List - II (P) A = 1 5 ∘ (1) All

Question

A prism of refracting angle A is made of material of refractive index 2. Assume rays are incident 'i' at angle of incidence such that $0 \leq i \leq 9 0^{\circ}$ .

List - I	List - II
(P) $A = 1 5^{\circ}$	(1) All rays are reflected back from second surface.
(Q) $A = 4 5^{\circ}$	(2) All rays are refracted into air from second surface.
(R) $A = 7 0^{\circ}$	(3) Some rays are reflected back from second surface.
(S) $A = 5 0^{\circ}$	(4) Some rays are refracted into air from second surface
	(5) No total internal reflection takes place at the second surface.

TestHub · Accepted Answer

Critical angle: C = sin − 1 2 1 ​ = 3 0 ∘ . At the second surface r 2 ​ = ∣ A − r 1 ​ ∣ with 0 ≤ r 1 ​ ≤ 3 0 ∘ . (P) A=15°: r 2 ​ ≤ 1 5 ∘ < C always, so no TIR; all rays refract out - 2, 5. (Q) A=45°: r 2 ​ ∈ [ 1 5 ∘ , 4 5 ∘ ] ; TIR when r 1 ​ < 1 5 ∘ - some reflected, some refracted - 3, 4. (R) A=70°: r 2 ​ ∈ [ 4 0 ∘ , 7 0 ∘ ] > C - all reflected back - 1. (S) A=50°: r 2 ​ ∈ [ 2 0 ∘ , 5 0 ∘ ] - mixed - 3, 4. Hence option (A).

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