Question

A vessel of depth x is half filled with oil of refractive index ${\mu }_2.$ and half with water of refractive index ${\mu }_1.$ 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 $\frac{x({\mu }_1+{\mu }_2)}{2{\mu }_1{\mu }_2}$

$\text{Refractive index}\mu =\frac{\text{Real depth}}{\text{Apparent depth}}\therefore \text{Apparent depth of the vessel when}\text{viewed from above is}{d}_{\text{apparent}}=\frac{x}{2{\mu }_1}+\frac{x}{2{\mu }_2}=\frac{x}{2}(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})=\frac{x}{2}\left(\frac{{\mu }_2+{\mu }_1}{{\mu }_1{\mu }_2}\right)=\frac{x({\mu }_1+{\mu }_2)}{2{\mu }_1{\mu }_2}$