Question

An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in figure. The breaker height is 3h and its radius h. when the beaker is filled with a liquid upto a height 2 h, he can see the lower end of the rod. Then refractive index of the liquid is

• A. $\frac{5}{2}$
• B. $\sqrt{\left(\frac{5}{2}\right)}$
• C. $\sqrt{\left(\frac{3}{2}\right)}$
• D. $\frac{3}{2}$

Answer 1

The correct option is B

$\sqrt{\left(\frac{5}{2}\right)}$

$\mu =\frac{sin{45}^{\circ }}{sinr}$

From figure, $sinr=\frac{h}{h\sqrt{5}}$

$\therefore \mu =\frac{\frac{1}{\sqrt{2}}\times h\sqrt{5}}{h}=\frac{\sqrt{5}}{\sqrt{2}}=\sqrt{\left(\frac{5}{2}\right)}$