Question 114: Ray Optics

Question

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 _________.

Accepted Answer

from $$\Delta OCB,\,	an 	heta  = {{CB} \over {OC}} = {R \over R} = 1$$
$$ \Rightarrow 	heta  = 45^\circ $$
We know, $$\sin c = {1 \over \mu }$$
for minimum $\mu$, sinc maximum $\Rightarrow$ C maximum
Here, $${c_{\max }} = 	heta  = 45^\circ $$
So, $$\mu  = {1 \over {\sin 45^\circ }} = {1 \over {{1 \over {\sqrt 2 }}}}$$
$$ \Rightarrow \mu  = \sqrt 2 $$

Answer

$\frac{3}{2}$

Answer

$\frac{\sqrt{3}}{2}$

Answer

$\sqrt{3}$

Answer

$\sqrt{2}$

Ray Optics

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