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. $\frac{2x({\mu }_1+{\mu }_2)}{{\mu }_1{\mu }_2}$
• E. $\frac{4({\mu }_1+{\mu }_2)x}{{\mu }_1{\mu }_2}$

Answer 1

Answer: (A)

Apparent depth
$=\frac{\text{Real}\text{depth}}{\mu }$
For oil apparent depth
$=\frac{x}{2{\mu }_1}$
and for water apparent depth
$=\frac{x}{2{\mu }_2}$
The apparent depth of the vessel
$=\frac{x}{2{\mu }_1}+\frac{x}{2{\mu }_2}$
$=\frac{x}{2}\left[\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}\right]=\frac{x}{2}\left[\frac{{\mu }_1+{\mu }_2}{{\mu }_1{\mu }_2}\right]$