Question

The lower half of a vessel of depth $2dcm$ 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. $2d\left(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}\right)$
• D. $2d\left(\frac{1}{{\mu }_1{\mu }_2}\right)$

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 $d_{app}=\frac{d_1}{{\mu }_1}+\frac{d_2}{{\mu }_2}$
Here, $d_1=d_2=d$
$\therefore d_{app}=\frac{d}{{\mu }_1}+\frac{d}{{\mu }_2}$
$=d\left(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}\right)$