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MHT CET 2021 (24 Sep, Shift 2) · Prism, Dispersion & Scattering

Prism, Dispersion & Scattering question from MHT CET 2021 (24 Sep, Shift 2)

Q64MHT CET 2021 · 24 SEP · SHIFT 2Medium

Prism, Dispersion & Scattering

A ray of light is incident on one face of an equilateral glass prism having refractive index 2\sqrt{2}. It produces the emergent ray which just. grazes along the adjacent face. The value of angle of incidence is (sin⁡45∘=cos⁡45∘=12)\left(\sin 45^\circ = \cos 45^\circ = \frac{1}{\sqrt{2}}\right)

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Answer: (d)

  1. Grazing emergence: r2=Cr_2 = C, sin⁡C=12⇒r2=45∘\sin C = \frac{1}{\sqrt{2}} \Rightarrow r_2 = 45^\circ.
  2. r1=60∘−45∘=15∘r_1 = 60^\circ - 45^\circ = 15^\circ
  3. sin⁡i=2sin⁡15∘⇒i=sin⁡−1(2sin⁡15∘)\sin i = \sqrt{2}\sin 15^\circ \Rightarrow i = \sin^{-1}(\sqrt{2}\sin 15^\circ)
  4. So the answer is (d).
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