Question

An object is placed at a distance of 40 cm

from a concave mirror of focal length 15 cm.

If the object is displaced through a distance

of 20 cm towards the mirror, the

displacement of the image will be

Accepted Answer

**Sol.** [Insert diagram of concave mirror with object O at 40 cm and focal length f = 15 cm]

$$\frac{1}{f} = \frac{1}{v_1} + \frac{1}{u}$$

$$-\frac{1}{15} = \frac{1}{v_1} - \frac{1}{40}$$

$$\Rightarrow \frac{1}{v_1} = \frac{1}{-15} + \frac{1}{40}$$

$$v_1 = -24 	ext{ cm}$$

When object is displaced by 20 cm towards mirror.

Now,
$$u_2 = -20$$

$$\frac{1}{f} = \frac{1}{v_2} + \frac{1}{u_2}$$

$$\frac{1}{-15} = \frac{1}{v_2} - \frac{1}{20}$$

$$\frac{1}{v_2} = \frac{1}{20} - \frac{1}{15}$$

$$v_2 = -60 	ext{ cm}$$

So, image shifts away from mirror by $= 60 - 24 = 36 	ext{ cm}$.