Question

If an object moves towards a plane mirror with speed '$v$' then:

• A. The image moves towards the mirror with a speed $v$
• B. The image moves away from the mirror with a speed $v$
• C. The image moves towards the mirror with a speed $2v$
• D. The image moves away from the mirror with a speed $2v$

Answer 1

The correct option is A The image moves towards the mirror with a speed $v$

Distance of Image formed in the mirror is same as the distance of the object form the surface of the mirror.

Thus is distance of object = u

Then distance of image = -u (as the image is formed at other side of the mirror)

Thus distance between image and object = 2u ...(1)

Now if mirroe is approaching you/object with speed v, then distance travelled by mirror in unit time = v units

Thus distance between mirror and object in unit time = u - v

Thus disatnce between object and its image = 2(u-v)....(2)

From equations (1) and (2) distance between image and object is reduced by 2v units in unit time(1 second)

Thus speed of image w.r.t object = 2v

so in this case The image moves towards the mirror with a speed v