Optics 2 Question 10
10. An observer can see through a pin-hole the top end of a thin rod of height $h$, placed as shown in the figure. The beaker height is $3 h$ and its radius $h$. When the beaker is filled with a liquid up to a height $2 h$, he can see the lower end of the rod. Then the refractive index of the liquid is
(2002, 2M)
(a) $\frac{5}{2}$
(b) $\sqrt{\frac{5}{2}}$
(c) $\sqrt{\frac{3}{2}}$
(d) $\frac{3}{2}$
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Answer:
Correct Answer: 10. (b)
Solution:
$$ \begin{aligned} & P Q=Q R=2 h \Rightarrow \angle i=45^{\circ} \\ & \therefore \quad S T=R T=h=K M=M N \\ & \text { So, } \quad K S=\sqrt{h^{2}+(2 h)^{2}}=h \sqrt{5} \\ & \therefore \quad \sin r=\frac{h}{h \sqrt{5}}=\frac{1}{\sqrt{5}} \end{aligned} $$
$$ \therefore \quad \mu=\frac{\sin i}{\sin r}=\frac{\sin 45^{\circ}}{1 / \sqrt{5}}=\sqrt{\frac{5}{2}} $$
