Question

A vessel is half-filled with a liquid of refractive index $ \mu $ . The other half of the vessel is filled with an immiscible liquid of refractive index $1.5\, \mu $ . The apparent depth of the vessel is $50\%$ of the actual depth. Then $ \mu $ is

• A. 1.4
• B. 1.5
• C. 1.6
• D. 1.67

Answer 1

Answer: (D)

Let $d$ be the depth of two liquids Apparent depth,
$\frac{d}{2 \mu}+\frac{d}{2(1.5 \mu)}=\frac{d}{2}$
Or $\frac{1}{\mu}+\frac{2}{3 \mu}=1$
$\Rightarrow \frac{3+2}{3 \mu}=1$
$\therefore \mu=\frac{5}{3}=1.67$