Question

If the mirror moves away from the object with speed $v$ units, then find the speed of the image that moves away from the object.

Answer 1

Step 1: Ray diagram

$AB$ is plane mirror

Step 2: Finding the speed of the image:

Let $u$ be the distance of the object and $-u$ be a distance of the image

Distance between image and object $=$ $2u$……..$\left(1\right)$

When the mirror moves away from the object with speed $v$ , the distance traveled will be $v$ units

Now, the distance between mirror and object is $=$ $u+v$

Distance between object and image is $=$ $2\left(u+v\right)$ …….$\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$

Distance moved by the image from object $=$$2u+2v-2u=2v$

Hence, the speed of the image that moves away from the object is $2v$ units