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At the interface between two materials having refractive indices (n₁ ) and (n₂ ), the critical angle for reflection of an em wave is ( _ 1 C ). The (n₂ ) material is replaced by another material having refractive index (n₃ ) such that the critical angle at the interface between (n₁ ) and (n₃ ) materials is ( _ 2 C ). If ( n ₃ n ₂ n ₁ ; n ₂ n ₃ = 2 5 ) and ( _ 2 C - _ 1 C = 1 2 ), then ( _ 1 C ) is

Options

  1. A( ⁻¹ ( 1 6 ) )
  2. B( ⁻¹ ( 1 3 ) )
  3. C( ⁻¹ ( -5 6 ) )
  4. D( ⁻¹ ( 2 3 ) )

Correct answer

C. ( ⁻¹ ( -5 6 ) )

Step-by-step solution

aligned & _ 1 C = n₁ n₂ & _ 2 C = n₁ n₃ & _ 2 C - _ 1 C = 1 2 aligned aligned & n ₁ n ₂ n ₃ - n ₁ n ₂ = 1 2 & n ₁ n ₂ n ₃ - n ₁= n ₂ 2 & n ₁ ( 2 5 -1 )= n ₂ 2 & n ₁ n ₂ = -5 6 & = ⁻¹ (- 5 6 ) aligned

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