Question

If an observer is walking away from the plane mirror with $6\,m/s$ . Then the velocity of the image with respect to the observer will be
A. $6\,m/s$
B. $ - 6\,m/s$
C. $12\,m/s$
D. $3\,m/s$

Answer 1

Hint: Here we have to find the relative velocity of the image with respect to the observer who is walking away from the plane mirror with a certain velocity that is already given in the question above. Use the formula of relative velocity in case of object and image moving away from the plane mirror.

Formula used:
The expression of relative velocity (${v_R}$) is,
${v_R} = {v_A} - {v_B}$
Here, ${v_A}, {v_B}$ are the velocities of object A and B.

Complete step by step solution:
We know that when an object is placed in front of a plane mirror, the plane mirror reflects light which helps in forming an image of the object behind the plane mirror and the image thus formed is located at the same distance as the object is present before the plane mirror. This was the case when the object placed in front of the plane mirror is not moving.

When the object placed in front of the plane mirror is moving away from the mirror then in that case the image of the object formed behind the plane mirror will also move and with the same velocity of the object that is placed in front of the plane mirror. Hence if the velocity of the object placed in front of the mirror is v then the image formed will also move with the same velocity v.

Now the velocity of observer(object) here is given,
$v = 6m/s$
Therefore the velocity of the image will also be,
$v = 6m/s$
We know the formula of relative velocity is,
${v_R} = {v_A} - {v_B}$
Putting all the values, we get;
${v_R} = 6 - ( - 6) = 12$
$\therefore {v_R} = 12\,m/s$

Hence the correct answer is option C.

Note: When the object placed in front of the plane mirror is moving towards the mirror then in that case the image of the object formed behind the plane mirror will move with the double velocity of the object that is placed in front of the plane mirror.