Question

If you run away from a plane mirror at 3.60 m\(/\)s, at what speed does your image move away from you?

Short answer

Your image moves away from you at 7.20 m/s.

Step-by-step solution

Understanding the problem

A plane mirror creates an image that appears to be at the same distance from the mirror as the object, but on the opposite side. The critical point is that both the object and the image move with respect to the mirror.

Identifying the movement

If you move away from the mirror at a speed of 3.60 m/s, your image also moves on the other side of the mirror. Both you and the image are moving relative to the mirror.

Calculating the speed of the image

As you move away from the mirror, your image moves at the same speed relative to the mirror but in the opposite direction. Therefore, the image also moves at 3.60 m/s relative to the mirror.

Determining the relative speed between you and your image

Since you and your image both move at 3.60 m/s away from the mirror, the relative speed of separation is the sum of your speed and the speed of the image: \[ ext{Relative speed} = 3.60 ext{ m/s} + 3.60 ext{ m/s} = 7.20 ext{ m/s} \]

Key concepts

Understanding Image Formation in Plane Mirrors

When you stand in front of a plane mirror, a fascinating phenomenon occurs. The mirror creates an image that looks just like you but appears to be located on the opposite side of the mirror. This image appears at the same distance from the mirror as you are on this side. Plane mirrors produce virtual images, meaning they cannot be projected on a screen because the light does not actually pass through the image location. The image in a plane mirror is always upright and reversed from left to right.

When you move, the image moves too. If you move towards the mirror, the image seems to come closer to you, and if you move away, the image seems to move further away. This direct relation between your movement and the image's movement is essential in understanding how images are formed by plane mirrors.

Exploring Relative Speed with Mirrors

Relative speed can be a little tricky in mirror scenarios, but it becomes clearer once we break it down. **Relative speed** refers to how fast one object is moving compared to another. In the context of a plane mirror, imagine you are running away from the mirror at a speed of 3.60 m/s. The key idea is that not only are you moving, but your mirror image is also moving away at the same speed.

The image appears to be on the opposite side, but both you and your image have a relative motion with respect to the mirror itself. When we talk about the relative speed between you and the image, we add your speed and the image's speed together. So, if both are moving away from the mirror at 3.60 m/s, the relative speed of separation is 3.60 m/s plus 3.60 m/s, making it 7.20 m/s. This total gives the combined speed at which you and your image pull away from each other.

Key Optics Concepts in Image Reflection

Optics is the branch of science that deals with light and its interactions. The concept of reflection is a central idea in optics and is easily observed in plane mirrors. When light hits a mirror, it bounces back, creating a reflection. This reflection allows us to see images in the mirror.

• **Law of Reflection:** This law states that the angle of incidence (the angle between the incoming light and the normal to the surface) is equal to the angle of reflection (the angle between the reflected light and the normal).
• **Virtual Images:** These are images formed where rays of light appear to meet or come from after reflection, even though they do not really meet at any actual point. The image is perceived behind the plane mirror.
• **Reversal of Images:** In plane mirrors, images are laterally inverted, meaning your left hand appears as your right hand in the reflection.

Understanding these principles helps clarify how images form and move with mirrors, and why reflection leads to the fascinating visual displays we see with plane mirrors.