Question

A vessel of depth x is half filled with oil 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

Answer: (A)

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

As refractive index, $\mu =\frac{Realdepth}{Apparentdepth}$
$\therefore$ Apparent depth of the vessel when viewed from above is
$d_{apparent}=\frac{x}{2{\mu }_1}+\frac{x}{2\mu 2}$
$=\frac{x}{2}(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})$
$=\frac{x}{2}\left(\frac{{\mu }_2+{\mu }_1}{{\mu }_1{\mu }_2}\right)=\frac{x({\mu }_1+{\mu }_2)}{2{\mu }_1{\mu }_2}$