Question

The image of a point source $\text{O}$ placed at the bottom of the container filled with water is formed at $I$ as shown in the figure. Find the focal length of the mirror.

• A. $15\text{cm}$
• B. $18\text{cm}$
• C. $25\text{cm}$
• D. $30\text{cm}$

Answer 1

The correct option is B $18\text{cm}$

We know that, $\text{Apparent depth}=\frac{\text{Actual depth}}{\mu }$

So, the object distance , $u=15+\frac{33.25}{\mu }$

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

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

Image distance,

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

$\Rightarrow v=15+\frac{25}{1.33}=33.75\text{cm}$

Using mirror formula:$$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$$$\Rightarrow \frac{1}{f}=\frac{1}{-\left(40\right)}+\frac{1}{-\left(33.75\right)}$

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

Hence, option (b) is the correct answer.