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Question:

A planar structure of length L and width W is made of two different optical media of refractive indices n1=1.5 and n2=1.44 as shown in figure. If L>>W, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For L=9.6m, if the incident angle θ is varied, the maximum time taken by a ray to exit the plane CD is t × 10⁻⁹s, where t is _________. [Speed of light c=3 × 10⁸m/s]

50.00

Solution:

Correct option is A. 50.00
1.5sinθc = 1.44sin90°
sinθc = 1.44/1.50 = 24/25
∴sinθc = x/d = 24/25
d = 25x/24
∴Total length travel by light = 25/24 × 9.6 = 10m
∴t = S/(Cn1) = 10/(3 × 10⁸/1.5) = 12 × 10⁻⁷ = 5 × 10⁻⁸
t = 50ns
t = 50 × 10⁻⁹
∴Answer = 50.