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MHT CET 2023 (9 May, Shift 2) · Refraction, Glass Slab & Apparent Depth

Refraction, Glass Slab & Apparent Depth question from MHT CET 2023 (9 May, Shift 2)

Q42MHT CET 2023 · 9 MAY · SHIFT 2Medium

Refraction, Glass Slab & Apparent Depth

If a ray of light in denser medium strikes a rarer medium at angle of incidence ii, the angles of reflection and refraction are rr and r′r' respectively. If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is

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Answer: (b)

  1. Reflected and refracted rays perpendicular: r+r′=90∘r + r' = 90^\circ, and r=ir = i.
  2. Snell (denser to rarer): μsin⁡i=sin⁡r′=cos⁡i⇒tan⁡i=1μ\mu\sin i = \sin r' = \cos i \Rightarrow \tan i = \frac{1}{\mu}.
  3. sin⁡C=1μ=tan⁡i=tan⁡r\sin C = \frac{1}{\mu} = \tan i = \tan r
  4. So the answer is (b) sin⁡−1(tan⁡r)\sin^{-1}(\tan r).
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