Verified Solution • 2025–26 Session moderate

QJEEM25Ph3340: JEE Main 2025 Physics - Class 12 JEEM25Ph3340 Solution: 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 _________.

JEE Main 2025 (Online) 28th January Morning Shift Physics - Geometrical Optics Question 1 English

Multiple Choice Options

  • A 32\frac{3}{2}
  • B 32\frac{\sqrt{3}}{2}
  • C 3\sqrt{3}
  • D 2\sqrt{2}

Step-by-Step Verified Solution

JEE Main 2025 (Online) 28th January Morning Shift Physics - Geometrical Optics Question 1 English Explanation

from ΔOCB, tan⁡θ=CBOC=RR=1\Delta OCB,\,\tan \theta = {{CB} \over {OC}} = {R \over R} = 1

⇒θ=45∘\Rightarrow \theta = 45^\circ

We know, sin⁡c=1μ\sin c = {1 \over \mu }

for minimum μ\mu , sinc maximum ⇒\Rightarrow C maximum

Here, cmax⁡=θ=45∘{c_{\max }} = \theta = 45^\circ

So, μ=1sin⁡45∘=112\mu = {1 \over {\sin 45^\circ }} = {1 \over {{1 \over {\sqrt 2 }}}}

⇒μ=2\Rightarrow \mu = \sqrt 2

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