Question

A vessel of depth $x$ is half filled with oil of refractive index ${\mu }_1$ and the other half is filled with water of refractive index ${\mu }_2$. The apparent depth of the vessel when viewed from above is:

• A. $\frac{x({\mu }_1+{\mu }_2)}{2{\mu }_1{\mu }_2}$
• B. $\frac{x{\mu }_1{\mu }_2}{2({\mu }_1+{\mu }_2)}$
• C. $\frac{x{\mu }_1{\mu }_2}{({\mu }_1+{\mu }_2)}$
• D. $\frac{2x({\mu }_1+{\mu }_2)}{{\mu }_1{\mu }_2}$

Answer 1

The correct option is A $\frac{x({\mu }_1+{\mu }_2)}{2{\mu }_1{\mu }_2}$

The relation between the real and apparent depth is:

$\mu =\frac{\text{Real Depth}}{\text{Apparent length}}$

So, apparent depth of the vessel when viewed from above is

$d_{apparent}=\frac{x}{2u_1}+\frac{x}{2u_2}$

$=\frac{x}{2}(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})$

$=\frac{x}{2}\left(\frac{{\mu }_2+{\mu }_1}{{\mu }_1{\mu }_2}\right)=\left(\frac{x({\mu }_1+{\mu }_2)}{2{\mu }_1{\mu }_2}\right)$