Question

A man runs towards a mirror at a speed of $15\,m/s$. What is the speed of his image?
A. $7.5\,m/s$
B. $15\,m/s$
C. $30\,m/s$
D. $45m/s$

Answer 1

Hint:Here we have to find the relative velocity of the image with respect to the man who is walking towards the plane mirror with a certain speed that is already given in the question above. We have to find the relation of relative speed in case of object and image moving towards the plane mirror.

Formula used:
Velocity of image with respect to object can be represented by:
${{v}_{IO}}={{v}_{I}}-{{v}_{O}}$
Here ${{v}_{IO}}$ denotes velocity of image with respect to object.
${{v}_{I}}\And {{v}_{O}}$ represents velocity of the image and object respectively.

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 towards the mirror then in that case the image of the object formed behind the plane mirror will also move and with the double 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 move with the double velocity 2v. Now the speed of man(object) here is given
$v = 15\,m/s$
Therefore, the speed of the image will be:
${v_i} = 2v = 2 \times 15 = 30$
$\therefore {v_i} = 30\,m/s$

Hence the correct answer is option C.

Note:There are so many ways in which an object can move in front of a plane mirror such as when object is moving parallel to the surface of mirror, perpendicular to the surface of mirror, velocity of an object is at some angle to the mirror etc. Therefore students must have to understand each concept carefully so that they are able to deal with any problem related to it.