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The x - z plane separates two media A and B of refractive indices n 1 = 1.5 and n 2 = 2 . A ray of light travels from A to B . Its directions in the two media are given by unit vectors µ → 1 = a i ^ + b j ^ , µ → 2 , = c i ^ + d j ^ , then -

Options

  1. Aa c = 4 3
  2. Ba c = 3 4
  3. Cb d = 4 3
  4. Db d = 3 4

Correct answer

A. a c = 4 3

Step-by-step solution

n 1 s i n i = n 2 s i n r 1.5 μ → 1 × j ^ = 2 μ → 2 × j ^ 1.5 [ ( a i ^ + b j ^ × j ^ ] = 2 [ ( c i ^ + d j ^ ) × j ^ ] 1.5 a k ^ = 2 c k ^ a c = 2 1.5 = 4 3

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