Chapter 29, Problem 49A

Suppose you walk toward a mirror at 1 m/s. How fast do you and your image approach each other? (The answer is not 1 m/s.)

To determine

To calculate: the speed of approach towards each other, if a person walks towards the mirror with $1m/s$

Explanation of Solution

Introduction: 

The image behind the mirror is known as a virtual image. The virtual image cannot be projected. Generally, a virtual image occurs when the light rays do not meet the object. But a person can see the image due to the eyes that project light rays back. 

Explanation: 

When a person is assumed to be at a distance of $2m$ away from the mirror, then a virtual image would appear behind the mirror at the same distance of $2m$ . So, the total distance of the image from the person is $4m\left(2m+2m\right).$

Considering the similar concept, if a person moves towards the mirror at a speed of $1m/s$ , that means the image behind the mirror also approaches with the same speed of $1m/s$ . Thus, a person and his image are approaching each other at a rate of 2 meters per second.

Conclusion: 

The person and image can approach $2m/s$ with each other when a person moving with $1m/s$ towards the mirror.