Question

In a thin spherical fish bowl of radius $10cm$ filled with water of refractive index $\frac{4}{3}$, there is a fish at a distance of $4cm$ there is a small fish at a distance of $4cm$ form the center $C$ as shown. The image of the fish appears, when seen from the point $D$ would be

• A. $5.2cm$
• B. $4.8cm$
• C. $2.6cm$
• D. $7.4cm$

Answer 1

The correct option is A $5.2cm$

$v\to imageposition$

$u\to objectposition$

$R\to Radiusofsurface$

$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

$\Rightarrow \frac{1}{v}-\frac{\left(4/3\right)}{\left(-6\right)}=\frac{1-4/3}{\left(-10\right)}$

$\Rightarrow \frac{1}{v}+\frac{4}{3\times 6}=\frac{1}{3\times 10}$

$\Rightarrow \frac{1}{v}=\frac{1}{30}-\frac{4}{18}$

$\Rightarrow \frac{1}{v}=\frac{-17}{90}$

$\Rightarrow v=\frac{-90}{17}=5.2cm$

Hence,

option $\left(A\right)$ is correct answer.