Question

The lower half of a vessel of depth $2d\, cm$ is 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. $d\left(\frac{\mu_{1} \mu_{2}}{\mu_{1}+\mu_{2}}\right)$
• B. $d\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right)$
• C. $2 d\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right)$
• D. $2 d\left(\frac{1}{\mu_{1} \mu_{2}}\right)$

Answer 1

Answer: (B)

If immiscible liquids of refractive indices $\mu_{1}$ and $\mu_{2}$ are filled in a vessel and their real depths are $d_{1}$ and $d_{2}$ as shown below

Then, apparent depth of the vessel seen perpendicularly is given as $d_{a p p}=\frac{d_{1}}{\mu_{1}}+\frac{d_{2}}{\mu_{2}}$
Here, $d_{1}=d_{2}=d$
$\therefore d_{ app }=\frac{d}{\mu_{1}}+\frac{d}{\mu_{2}}$
$=d\left(\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}\right)$