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)

1.67

Let d be the depth of two liquids , Then apparent depth

$\frac{\left(d/2\right)}{\mu }+\frac{\left(d/2\right)}{1.5\mu }=\frac{d}{2}$

or

$\frac{1}{\mu }+\frac{2}{3\mu }=1$

Solving we get $\mu =1.671$