A planar structure of length L and width W is made of two different optical media of refractive indices n 1 = 1.5 and n 2 = 1.44 as shown in figure. If L > > W , a ray entering from end A B will emerge from end C D only if the total internal reflection condition is met inside the structure. For L = 9.6 m , if the incident angle θ is varied, the maximum time taken by a ray to exit the plane C D is t × 10 - 9 s , where

Step-by-step solution

For maximum time taken by a rat to exit, it must travel maximum distance. So, for this, it should be incident at minimum possible angle i.e., θ C at n 1 - n 2 boundary. Applying Snells' law at n 1 - n 2 boundary ⇒ 1.5 s i n θ C = 1.44 s i n 90 ° ⇒ s i n θ C = 1.44 1.50 = 24 25 ∴ s i n θ C = x d = 24 25 ⇒ d = 25 x 24 ∴ total length travel by light = 25 25 × 9.6 = 10 m a s , x m a x = L = 9.6 m ∴ t = S C n 1 = 10 3 × 10 n 1.5 t = distance travelled speed of light in medium = 1 2 × 10 - 7 = 5 × 10 - 9 s e c o n d s t