Question

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 $3h$ and its radius $h$. When the beaker is filled with a liquid up to a height $2h$. he can see the lower end of the rod. Then the refractive index of the liquid is:

• A. $5/2$
• B. $\sqrt{5/2}$
• C. $\sqrt{3/2}$
• D. $3/2$

Answer 1

The correct option is B $\sqrt{5/2}$

From the figure, $PQ=QR=2h$

$\therefore \angle i=45°$

$ST=RT=h=KM=MN$

$\therefore KS=\sqrt{h^2+{\left(2h\right)}^2}=h\sqrt{5}$

$\therefore \sin r=\frac{h}{h\sqrt{5}}=\frac{1}{\sqrt{5}}$

Now, $\mu =\frac{\sin i}{\sin r}=\frac{\sin 45°}{\frac{1}{\sqrt{5}}}=\sqrt{\frac{5}{2}}$