Question

In a thin spherical fish bowl of radius $10cm$ filled with water of refractive index $\frac{4}{3}$ there is a small fish at a distance of $4cm$ form the center $C$ as shown in figure. Where will the image of fish appears, if seen from $E$

• A. $5.2cm$
• B. $7.2cm$
• C. $4.2cm$
• D. $3.2cm$

Answer 1

Answer: (A)

$5.2cm$

Whow that

$\frac{{\mu }_2}{V}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\therefore {\mu }_1=\frac{4}{3},{\mu }_2=1$

$u=-6cm,v=\text{to find}\left\{u\text{is from}6\right\}$

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

$\begin{array}{c}\Rightarrow \frac{1}{v}+\frac{4}{3\cdot 6}=\frac{3-4}{3\cdot 10}\\ \Rightarrow \frac{1}{v}=\frac{-1}{30}-\frac{4}{18}\\ \Rightarrow \frac{1}{v}=\frac{-3-20}{90}\\ \therefore v=\frac{-90}{23}\\ \Rightarrow v=-5.2cm\end{array}$

- ve sign is due to left of 6

Hence (A) is correct option.