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 $\frac{1}{\mu }+\frac{2}{3\mu }=1$
$\Rightarrow \frac{3+2}{3\mu }=1$
$\therefore \mu =\frac{5}{3}=1.67$