Question

A vessel of depth $2 d\, cm$ is half filled with a liquid of refractive index $\mu_{1}$ and the upper half with a liquid of refractive index $\mu_{2}$. The apparent depth of the vessel seen perpendicularly is

• A. $\left(\frac{\mu_{1} \mu_{2}}{\mu_{1}+\mu_{2}}\right) d$
• B. $\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right) d$
• C. $\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right) 2 d$
• D. $\left(\frac{1}{\mu_{1} \mu_{2}}\right) d$

Answer 1

Answer: (B)

Apparent depth $=\frac{\text { real depth }}{\text { refractive index }}$
$\Rightarrow $ depth seen $=\frac{d}{\mu_{1}}+\frac{d}{\mu_{2}}$
$=d\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right)$