Question

An observer can see through a pin-hole the top end of a thin rod of height A, 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. $\frac{5}{2}$
• B. $\sqrt{\frac{5}{2}}$
• C. $\sqrt{\frac{3}{2}}$
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

$\sqrt{\frac{5}{2}}$

Answer 2

$$PQ = QR = 2h$$ $$\therefore \quad \angle i = 45^\circ$$ $$\therefore \quad ST = RT = h = KM = MN$$ $$\text{So,} \quad KS = \sqrt{h^2 + (2h)^2} = h\sqrt{5}$$ $$\therefore \quad \sin r = \frac{h}{h\sqrt{5}} = \frac{1}{\sqrt{5}}$$ $$\therefore \quad \mu = \frac{\sin i}{\sin r} = \frac{\sin 45^\circ}{1/\sqrt{5}} = \sqrt{\frac{5}{2}}$$