Reflection of light and the plane mirror

How do you see yourself in a mirror?

Look at a flat mirror. You see your face, your hair and the wall behind you. Look at a sheet of paper. You see the paper, but not your face. Both the mirror and the paper send light back to your eye. What is different?

To find out, we need the rules of reflection. Reflection is the bouncing back of light when it falls on a surface.

The words we use

Look at the picture.

• The ray that falls on the mirror is the incident ray.
• The ray that bounces back is the reflected ray.
• The normal is a line at right angles to the mirror, drawn at the point where the ray falls. This point is the point of incidence.
• The angle of incidence $i$ is the angle between the incident ray and the normal.
• The angle of reflection $r$ is the angle between the reflected ray and the normal.

Both angles are measured from the normal, and not from the surface of the mirror. This is a very common mistake.

The two laws of reflection

1. The angle of incidence is equal to the angle of reflection: $i = r$.
2. The incident ray, the normal and the reflected ray all lie in the same plane. For a flat page, this means that the three lines are on the paper and none of them comes out of it.

These laws are true for every kind of reflecting surface, flat or curved.

You should find that the two angles always match. At $0^\circ$ the ray goes straight back along the normal. At a large angle the ray only grazes the mirror. The angle between the two rays is always twice the angle of incidence.

Regular and diffuse reflection

A smooth surface, such as a mirror, sends parallel rays back as parallel rays. This is regular reflection. A rough surface, such as paper or a wall, has many small pieces turned in different directions. Each small piece obeys the law of reflection, but the normals point in different ways. So the reflected rays go in many directions. This is diffuse reflection.

Diffuse reflection is not a failure. It is the reason why you can see a wall or a book from any side. A mirror seems bright only when your eye is in the path of its reflected rays.

The image in a plane mirror

A plane mirror is a flat mirror. Look at the picture.

Two rays leave the top of the object, and the mirror reflects them. The reflected rays do not meet. They spread out, as if they came from a point behind the mirror. Your eye sees the image at this point. Light does not really come from there, and a screen placed there would stay dark. We call such an image a virtual image. A real image is one where the light really meets, and a screen can show it.

The image in a plane mirror has these properties:

• It is virtual and upright.
• It is as big as the object.
• It is as far behind the mirror as the object is in front of it.
• It is laterally inverted: the left of the object becomes the right of the image. This is why the word AMBULANCE is written in reverse on the front of the vehicle. The driver in front reads it correctly in the rear-view mirror.

A worked example

You stand $2\ \text{m}$ in front of a plane mirror. How far are you from your image?

1. The image. It is $2\ \text{m}$ behind the mirror.
2. The distance. From you to the image is $2\ \text{m} + 2\ \text{m} = 4\ \text{m}$.
3. Now walk $0.5\ \text{m}$ toward the mirror. You are $1.5\ \text{m}$ from the mirror, and the image is $1.5\ \text{m}$ behind it. You are $3\ \text{m}$ from the image.

So when you walk toward a mirror, your image comes toward you too. The gap shrinks twice as fast as you walk.

Practise with new numbers

Try it in Python

The program makes a table of the angle of incidence, the angle of reflection and the angle between the two rays.

Remember these

• The angle of incidence equals the angle of reflection, and both are measured from the normal.
• The incident ray, the normal and the reflected ray are in one plane.
• A plane mirror forms a virtual, upright image, of the same size, as far behind the mirror as the object is in front.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A ray makes an angle of $30^\circ$ with the surface of a plane mirror. What is the angle of reflection?

2. What is the difference between regular and diffuse reflection?

3. A boy stands $3\ \text{m}$ in front of a plane mirror. He walks $1\ \text{m}$ toward it. How far is he from his image?

4. You raise your right hand in front of a mirror. Which hand does your image raise?