NTA Abhyas JEE Main2020PhysicsRay OpticsPractice
A rectangular glass slab ABCD , of refractive index, n 1 , is immersed in water of refractive index n 2 ( n 1 > n 2 ) . A ray of light is incident at the surface AB of the slab, as shown. The maximum value of the angle of incidence α max , such that the ray comes out only from the other surface CD , is given by
Options
- Asin − 1 [ n 1 n 2 cos ( sin − 1 n 2 n 1 ) ]
- Bsin − 1 [ n 1 cos ( sin − 1 1 n 2 ) ]
- Csin − 1 ( n 1 n 2 )
- Dsin − 1 ( n 2 n 1 )
Correct answer
A. sin − 1 [ n 1 n 2 cos ( sin − 1 n 2 n 1 ) ]
Step-by-step solution
Consider the figure. The ray will come out from CD if it suffers a total internal reflection at surface AD , i.e., it strikes the surface AD at critical angle C (the limiting case). Applying Snell’s law at P , we get n 1 sin C = n 2 or sin C = n 2 n 1 Applying snell’s law at Q , we get n 2 sin α = n 1 cos C ; ⇒ sin α = n 1 n 2 cos sin − 1 ( n 2 n 1 ) or α = sin − 1 [ n 1 n 2 cos sin − 1 ( n 2 n 1 ) ]