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