Question

A vessel of depth $2d$ is half 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 perpendicular is

• A. $d\left(\frac{{\mu }_1{\mu }_2}{{\mu }_1+{\mu }_2}\right)$
• B. $d(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})$
• C. $2d(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})$
• D. $2d\left(\frac{1}{{\mu }_1{\mu }_2}\right)$

Answer 1

Answer: (B)

$d(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})$

Apparent depth $=\frac{\text{real depth}}{\text{refractive index}}$

$\Rightarrow$ depth seen $=\frac{d}{{\mu }_1}+\frac{d}{{\mu }_2}$

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