JEE Advanced 2023 Paper 2 Q05 Physics Waves & Optics Wave Optics Hard

JEE Advanced 2023 Paper 2 · Q05 · Wave Optics

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?

  1. A. It will deflect up by an angle $\tan^{-1}\left(\dfrac{(n_2^2 - n_1^2)d}{2h}\right)$.
  2. B. It will deflect up by an angle $\tan^{-1}\left(\dfrac{(n_2 - n_1)d}{h}\right)$.
  3. C. It will not deflect.
  4. D. The deflection angle depends only on $(n_2 - n_1)$ and not on the individual values of $n_1$ and $n_2$.
JEE Advanced multi-correct — pick every correct option, then check.
Reveal answer + step-by-step solution

Correct answer:B, D

Solution

Different parts of the wavefront travel at different speeds because $n$ varies linearly with height. The wavefront emerging from the slab tilts; the path-length difference between top and bottom is $\Delta = (n_2 - n_1)d$. Tilt angle $\tan\alpha = \Delta/h = (n_2-n_1)d/h$ — (B) TRUE. Since the deflection depends only on the difference $(n_2 - n_1)$ — (D) TRUE. (A) and (C) are FALSE.

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