Question

Final image of a point source $O$ placed at the bottom of the container filled with water in it is formed at $25\text{cm}$ below the water level as shown in the figure. Focal length of the mirror (in $\text{cm}$) is

• A. $-15$
• B. $-30$
• C. $-18$
• D. $-25$

Answer 1

The correct option is C $-18$

Using the concept of apparent depth,

Apparent depth $=\frac{\text{Actual depth}}{\mu }$

From question, object distance will be

$u=15+\frac{33.25}{\mu }=15+\frac{33.25}{1.33}$

$\Rightarrow u=40\text{cm}$

And image distance will be

$v=15+\frac{25}{\mu }=15+\frac{25}{1.33}$

$\Rightarrow v=33.80\text{cm}$

For concave mirror,
$u=-40\text{cm};v=-33.80\text{cm}$

By using mirror formula

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{f}=\frac{1}{-40}+\frac{1}{-33.75}$

$\therefore f\approx -18\text{cm}$

Hence, option $\left(b\right)$ is correct.