Question

A container is filled with water ($\mu =$1.33) upto a height of $33.25cm$. A concave mirror is placed $15cm$ above the water level and the image of an object placed at the bottom is formed $25cm$ below the water level. The focal length of the mirror is (nearly) :

• A. 10 cm
• B. 15 cm
• C. 19 cm
• D. 25 cm

Answer 1

The correct option is C 19 cm

One important thing to note in this question is that even after reflection from the mirror, there will be refraction. So, the image formation without water would have taken place at the apparent depth of the real image below the level of water.
So, for image formation, (by sign convention)
$-u=15+$ apparent depth of object
$-v=15+$ apparent depth of image

Apparent depth of object= $\frac{33.25}{1.33}=25cm$

$u=-40cm$

Apparent depth of image= $\frac{25}{1.33}=18.8cm$

$v=-33.8cm$

$\frac{1}{f}=\frac{1}{33.8}+\frac{1}{40}$

From this we get $f\approx 19cm$