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

Concept:

Concave Mirror is a spherical mirror having inward reflecting surface.

Concave mirror can form real as well as virtual images which depends upon the position of the object from the mirror.

Mirror formula is

\(\frac{1}{f} = \frac{1}{{{v}}} + \frac{1}{u}\)

where f, v, u is the focal length of mirror, image distance and object distance from the mirror respectively.

Calculation:

Given-

Object distance, u = -40 cm

Focal length, f = -15 cm

Image distance, v₁=?

\(\frac{1}{f} = \frac{1}{{{v_1}}} + \frac{1}{u}\)

\( - \frac{1}{{15}} = \frac{1}{{{v_1}}} - \frac{1}{{40}}\)

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

v₁ = -24 cm

When object is displaced by 20 cm towards mirror.

Now, 

u₂ = -20 cm

\(\frac{1}{f} = \frac{1}{{{v_2}}} + \frac{1}{{{u_2}}}\)

\(\frac{1}{{ - 15}} = \frac{1}{{{v_2}}} - \frac{1}{{20}}\)

\(\frac{1}{{{v_2}}} = \frac{1}{{20}} - \frac{1}{{15}}\)

v₂ = -60 cm

So, image shifts away from mirror by = 60 – 24 = 36 cm.