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JEE Advanced 2023Paper 2
Exam
JEE Advanced
Year
2023
Paper
Paper 2
Subject
Physics
Chapter
Ray Optics

JEE Advanced 2023 · Paper 2 · Physics · Ray Optics

A monochromatic light wave is incident normally on a glass slab of...

A monochromatic light wave is incident normally on a glass slab of thickness dd, as shown in the figure. The refractive index of the slab increases linearly from n1{n}_{1} to n2{n}_{2} over the height hh. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

A monochromatic light wave is incident normally on a glass slab of thickness d , as shown in the figure. The refractive

Options

  1. AIt will deflect up by an angle $\tan^{- 1}\left[\dfrac{\left({{n}_{2}}^{2} - {{n}_{1}}^{2}\right)d}{2h}\right]
  2. BIt will deflect up by an angle $\tan^{- 1}\left[\dfrac{\left({n}_{2} - {n}_{1}\right)d}{h}\right]
  3. CIt will not deflect
  4. DThe deflection angle depends only on (n2−n1)( {n}_{2} - {n}_{1} ) and not on the individual values of n1{n}_{1} and n2{n}_{2}

Correct answer

D. The deflection angle depends only on (n2−n1)( {n}_{2} - {n}_{1} ) and not on the individual values of n1{n}_{1} and n2{n}_{2}

Step-by-step solution

A monochromatic light wave is incident normally on a glass slab of thickness d , as shown in the figure. The refractive

Dashed line MNMN and PQPQ are incident wave front.

Just before entering the slab PQPQ is maxima.

P1{P}_{1} and Q1{Q}_{1} are the points on other face of slab.

So, P1{P}_{1} will be at a lead of n2d{n}_{2}d w.r.t. PP

and Q′Q ' will be at lead of n1d{n}_{1}d w.r.t. QQ

As the medium on the right side is homogeneous, so to have same path lead as P1,Q′{P}_{1}, Q ' must travel to Q1{Q}_{1}, such that n2d=n1d+hsinθ{n}_{2}d = {n}_{1}d + hsin\theta.

sinθ=(n2−n1)dh⇒θ=sin⁡−1[(n2−n1)dh]sin\theta = \dfrac{\left({n}_{2} - {n}_{1}\right)d}{h} ⇒ \theta = \sin^{- 1}\left[\dfrac{\left({n}_{2} - {n}_{1}\right)d}{h}\right]

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