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 Li

Step-by-step solution

aligned & = ( ₀- ₀ )+ (180-2 ₀ )+ ( ₀-2 ₀ ) & =180+2 ₀-4 ₀ aligned (P) =180+2 ₀-4 ₀180=180+2 ₀-4 ₀ ₀=2 ₀ ...(i) ₀=2 ₀ ...(ii) From (i) & (ii) aligned & ₀=2 ( ₀ / 2 ) ( ₀ 2 )=1 & ₀ 2 =0 & ₀=0 aligned (Q) ₀=2 ₀ ...(i) ₀= 3 ₀ ...(ii) From (i) & (ii) aligned & ₀= 3 ( ₀ 2 ) & ( ₀ 2 )= 3 2 & ₀ 2 =30,150 & ₀=60,300 (Rejected) & ₀=60 , 0 aligned (R) ₀=2 ₀ aligned & ₀= 3 ₀ & 2 ₀= 3 ₀ & ₀= 3 2 & ₀=30,150 (Rejected) aligned ₀=30, 0 ...(iii) aligned & (S) 45= 2 ₀ & ₀=1 / 2 & ₀=60 & =180+2 ₀-4 ₀ aligned =180+90-120 ...(iv) =180