Q39 / 51 · JEE Advanced 2023 (Paper 2) · Physics

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 n1 to n2 over the height h. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

Figure

  • A
    It will deflect up by an angle tan-1n22-n12d2h
  • B
    It will deflect up by an angle tan-1n2-n1dh
  • C
    It will not deflect
  • Correct answer
    D
    The deflection angle depends only on (n2-n1) and not on the individual values of n1 and n2

Solution

Figure

Dashed line MN and PQ are incident wave front.

Just before entering the slab PQ is maxima.

P1 and Q1 are the points on other face of slab.

So, P1 will be at a lead of n2d w.r.t. P

and Q' will be at lead of n1d w.r.t. Q

As the medium on the right side is homogeneous, so to have same path lead as P1, Q' must travel to Q1, such that n2d=n1d+h sinθ.

sinθ=n2-n1dh⇒θ=sin-1n2-n1dh

Hence, the correct answer is option: 'D'.

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