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JEE MainPhysicsRay Optics

A light ray undergoes symmetrical passage through a prism of angle A . If the angle of incidence on the first face is equal to the angle of the prism, the critical angle for the prism-air interface is

Options

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

Correct answer

D. ⁻¹ ( 1 2 ( A 2 ) )

Step-by-step solution

Symmetrical passage of a light ray through a prism implies that the prism is in the position of minimum deviation. In this state, the angle of refraction at the first face is r = A 2 . Given that the angle of incidence is i = A , we can find the refractive index of the prism material using Snell's law: = (i) (r) = (A) ( A 2 ) Using the double angle identity (A) = 2 ( A 2 ) ( A 2 ) , we get: = 2 ( A 2 ) ( A 2 ) ( A 2 ) = 2 ( A 2 ) The critical angle _c for the prism-air interface is given by ( _c) = 1 . ( _c) = 1 2

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