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JEE Main 2022 (29 Jul, Shift 2) · Refraction, Glass Slab & Apparent Depth

Refraction, Glass Slab & Apparent Depth question from JEE Main 2022 (29 Jul, Shift 2)

Q44JEE Main 2022 · 29 JUL · SHIFT 2Medium

Refraction, Glass Slab & Apparent Depth

Light enters from air into a given medium at an angle of 45∘45^\circ with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of 15∘15^\circ from its original direction. The refractive index of the medium is:

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Answer: (c)

  1. Ray makes 45∘45^\circ with the surface, so with the normal i=90∘−45∘=45∘i = 90^\circ - 45^\circ = 45^\circ.
  2. Deviation δ=i−r=15∘⇒r=30∘\delta = i - r = 15^\circ \Rightarrow r = 30^\circ.
  3. μ=sin⁡45∘sin⁡30∘=1/21/2=2=1.414\mu = \dfrac{\sin 45^\circ}{\sin 30^\circ} = \dfrac{1/\sqrt{2}}{1/2} = \sqrt{2} = 1.414.
  4. So the answer is (c) 1.414.
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