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JEE Main 202528 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
28 January
Shift
Morning Shift
Subject
Physics
Chapter
Ray Optics

JEE Main 2025 · 28 January · Morning Shift · Physics · Ray Optics

A hemispherical vessel is completely filled with a liquid of...

A hemispherical vessel is completely filled with a liquid of refractive index μ\mu. A small coin is kept at the lowest point (O)(\mathrm{O}) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is A hemispherical vessel is completely filled with a liquid of refractive index μ . A small coin is kept at the lowest

Options

  1. A3\sqrt{3}
  2. B32\frac{\sqrt{3}}{2}
  3. C32\frac{3}{2}
  4. D2\sqrt{2}

Correct answer

D. 2\sqrt{2}

Step-by-step solution

A hemispherical vessel is completely filled with a liquid of refractive index μ . A small coin is kept at the lowest
For the rays from coin to reach the point EE, the refracted rays must grazing the surface, i.e. they must be incident at critical angle θc\theta_c inside the liquid. μ=1sin⁡θc\mu=\frac{1}{\sin \theta_c} μ\mu is minimum when θc\theta_c is maximum. Maximum value of θc=45∘\theta_c=45^{\circ} ⇒μ\Rightarrow \mu has a minimum value of 2\sqrt{2}.
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