JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments
A hemispherical vessel is completely filled with a liquid of refractive index \(\mu\). A small coin is kept at the lowest point \((\mathrm{O})\) 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 \(\sqrt{3}\)
- B \(\frac{\sqrt{3}}{2}\)
- C \(\frac{3}{2}\)
- D \(\sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{2}\)
Step-by-step Solution
Detailed explanation
For the rays from coin to reach the point \(E\), the refracted rays must grazing the surface, i.e. they must be incident at critical angle \(\theta_c\) inside the liquid. \(\mu=\frac{1}{\sin \theta_c}\) \(\mu\) is minimum when \(\theta_c\) is maximum. Maximum value of…
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