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A ray of light travelling in a denser medium strikes the boundary of a rarer medium. The ray gets partially reflected and refracted. The angle of reflection is r and that of refraction is r ' . If the reflected and refracted rays make an angle of 90 ° with each other then the critical angle for the pair of media is

Options

  1. Asin -1 (tan r)
  2. Btan -1 (sin r)
  3. Csin -1 (tan r')
  4. Dtan -1 (sin r')

Correct answer

A. sin -1 (tan r)

Step-by-step solution

D μ R = sin r sin r ′ -----(1) At critical angle D μ R = sin C sin 90 o -----(2) from equation (1) & (2) sin C = sin r sin 90 - r ⇒ sin r = tan r ⇒ C = sin -1 tan r

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