# 2. A boy stands 10 m in front of a plane mirror . then be moves 3 m towards the mirror. How many metres does his image move towards him? A) 20 B) 14 C) 7 D) 6

Jan 24, 2018

D.6

#### Explanation:

The image formed in a plane mirror is as far behind the mirror as the object is in front of it, i.e. the distance between the object and the mirror $u$ is the same as the distance between the mirror and the image $v$.

So,here,given $u = 10$ hence $v = 10$ so distance between the image and the boy is $u + v$ or $20$ meters.

If the boy moves $3$ meters towards the mirror,then,$u = 10 - 3$ or $7$
So,$v = 7$ as well

Now,distance between the boy and his image is $7 + 7$ i.e $14$ meters.

So,the image moved to him by $\left(20 - 14\right)$ or $6$ meters

Alternatively,
From the above discussion,clearly,

$v + u = x$(let)=$2 u$
So, $x = 2 u$
Or, $\frac{\mathrm{dx}}{\mathrm{dt}} = 2 \frac{\mathrm{du}}{\mathrm{dt}}$

It means velocity of image should be twice than that of man's velocity,so if the man moves by $3 m$ then the image will move to him by $6 m$