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JEE Advanced2023PhysicsRay OpticsActual

A monochromatic light wave is incident normally on a glass slab of thickness d , as shown in the figure. The refractive index of the slab increases linearly from n 1 to n 2 over the height h . Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

Options

  1. AIt will deflect up by an angle tan - 1 n 2 2 - n 1 2 d 2 h
  2. BIt will deflect up by an angle tan - 1 n 2 - n 1 d h
  3. CIt will not deflect
  4. DThe deflection angle depends only on ( n 2 - n 1 ) and not on the individual values of n 1 and n 2

Correct answer

D. The deflection angle depends only on ( n 2 - n 1 ) and not on the individual values of n 1 and n 2

Step-by-step solution

Dashed line M N and P Q are incident wave front. Just before entering the slab P Q is maxima. P 1 and Q 1 are the points on other face of slab. So, P 1 will be at a lead of n 2 d w.r.t. P and Q ' will be at lead of n 1 d w.r.t. Q As the medium on the right side is homogeneous, so to have same path lead as P 1 ,   Q ' must travel to Q 1 , such that n 2 d = n 1 d + h   sin θ . sin θ = n 2 - n 1 d h ⇒ θ = sin - 1 n 2 - n 1 d h

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