Question

A fish is near the centre of a spherical fishbowl filled with water ( ${\mu }_w=4/3$ ). A child is standing at a distance of $2R$ from the centre of the bowl, where $R$ is the radius of curvature of the bowl. The distance from the centre of the fishbowl, where the child's nose will appear to the fish is

• A. $R$
• B. $2R$
• C. $3R$
• D. $4R$

Answer 1

Answer: (C)

$\frac{{\mu }_2}{\text{v}}-\frac{{\mu }_1}{\text{u}}=\frac{{\mu }_2-{\mu }_1}{\text{R}}\Rightarrow \frac{4}{3\text{v}}-\frac{1}{-\text{R}}=\frac{\frac{4}{3}-1}{\text{R}}\Rightarrow \frac{4}{3\text{v}}=\frac{1}{3\text{R}}-\frac{1}{\text{R}}$
$\frac{4}{3\text{v}}=\frac{1-3}{3\text{R}}\Rightarrow \text{v}=-\frac{4\text{R}}{2}\Rightarrow \text{v}=-2\text{R}$
Distance of image from centre = 3R