Question

A plane mirror is moved towards a stationary observer with a speed of $4m{s}^{-1}$. The speed with which his image will move towards him?

• A. $2m{s}^{-1}$
• B. $4m{s}^{-1}$
• C. $8m{s}^{-1}$
• D. The image will stay at rest

Answer 1

The correct option is C $8m{s}^{-1}$

Initially the distance of the image in mirror is same as the distance of the stationary observer from mirror (let $u$).

Distance of the observer from mirror $=u$

Distance of the image from mirror $=-u$ (other side of mirror)

Distance between observer and image $=2u$

Now as the mirror is approaching the stationary observer with speed (let $v$ m/s), the distance travelled by mirror in 1 second $=v$ m,

the distance between observer and mirror after 1 second $=(u-v)$ m ..............eq1

the distance between observer and its image after 1 second $=2(u-v)$ m ..............eq2

from eq1 and eq2, the distance between observer and image is reduced by $2v$ in 1 second, therefore speed of the image wrt observer will be $2v$.

Here, given $v=4m/s$

therefore speed of the image with which it approaches the stationary observer $=2v=2\times 4=8m/s$