Question

A particle goes in a circle of radius 2.0 cm. A concave mirror of focal length 20 cm is placed with its principal axis passing through the centre of the circle and perpendicular to its plane. The distance between the pole of the mirror and the centre of the circle is 30 cm. Calculate the radius of the circle formed by the image.

Answer 1

u = - 30 cm,

f = - 20 cm

We know, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{v}+-\frac{1}{30}=-\frac{1}{20}$

$\Rightarrow \frac{1}{v}=\frac{1}{30}-\frac{1}{20}=\frac{1}{60}$

$\Rightarrow v=60\text{cm}$

Image of the circle is formed at a distance 60 cm in front of the mirror.

$\therefore m=-\frac{v}{u}=\frac{R_{\text{image}}}{R_{\text{object}}}$

$\Rightarrow -\frac{(-60)}{(-30)v}=\frac{R_{\text{image}}}{2}$

$\Rightarrow R_{\text{image}}=4\text{cm}$

Radius of image of the circle is 4 cm.