A point source of light is 60 cm from a screen and is kept at the focus of a concave mirror which reflects light on the screen. The focal length of the mirror is 20 cm. The ratio of average intensities of the illumination on the screen when the mirror is present and when the mirror is removed is :

Let I₁, I₂ are intensities of light on the screen and on the mirror due to the source directly.

After reflection from the mirror, the light move parallel. Hence intensity on the screen due to reflected light is same as that of intensity on the mirror due to source directly (I₂).

$\mathrm{I}\propto \frac{1}{{\mathrm{d}}^2},\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}={\left(\frac{20}{60}\right)}^2\Rightarrow {\mathrm{I}}_2=9{\mathrm{I}}_1$

$\therefore$On the screen, intensity without mirror is I₁ only.

Intensity with mirror is ${\mathrm{I}}_1+{\mathrm{I}}_2={\mathrm{I}}_1+9{\mathrm{I}}_1=10{\mathrm{I}}_1$. The ratio is $10{\mathrm{I}}_1:{\mathrm{I}}_1=10:1$