Images formed by a convex mirror

The mirror on the side of a car

Look at the small mirror on the side of a car or a bus. Everything in it looks smaller, but it shows a wide part of the road behind. This mirror is a convex mirror.

The image in a convex mirror

Take an object in front of a convex mirror, and draw two rays from its top.

1. Ray 1 goes parallel to the principal axis. After reflection, it goes away as if it came from the focus $F$ behind the mirror.
2. Ray 2 is directed toward $F$ behind the mirror. After reflection, it goes parallel to the principal axis.

The two reflected rays spread out, so they do not meet in front of the mirror. We trace them back with dashed lines. The dashed lines meet behind the mirror. This point is the top of the image.

The image in a convex mirror is always:

• virtual, because the rays do not really meet,
• upright,
• smaller than the object,
• behind the mirror, between $P$ and $F$.

You should find that the image never leaves the space between $P$ and $F$. Far away, the object gives a tiny image near $F$. Close up, the image grows and moves toward $P$, but it stays smaller than the object.

This is true for every position of the object. When the object is at infinity, the image is a very small point at $F$. When the object comes closer to the mirror, the image moves away from $F$ toward $P$ and grows a little, but it never becomes as large as the object.

Why is a convex mirror used in vehicles?

A convex mirror curves outward. It collects rays from a wide region and shows them in a small image. So it has a wider field of view than a plane mirror of the same size. A driver can see more of the road behind. The image is smaller than the object, but this is the price for the wider view. The image is also upright, so the driver is not confused.

Convex mirrors are also used as security mirrors in shops, at blind turns of roads and in lifts, for the same reason.

A worked example

A convex mirror has a focal length of $12\ \text{cm}$. A cup stands $60\ \text{cm}$ in front of it. Where can the image be, and what is it like?

1. The rule. A convex mirror always gives an image between $P$ and $F$, behind the mirror.
2. So the image is less than $12\ \text{cm}$ behind the mirror.
3. What it is like: virtual, upright and smaller than the cup. (The formula in the next lesson gives $10\ \text{cm}$ behind the mirror.)

Concave and convex mirrors: how to tell them apart

Practise with new numbers

Try it in Python

The program finds the image in a convex mirror for an object at several distances.

Remember these

• A convex mirror always forms a virtual, upright and smaller image behind the mirror.
• It gives a wide field of view, so it is used as a rear-view mirror.
• Its focus is virtual and is behind the mirror.

Check yourself

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

1. Can a convex mirror form a real image?

2. You walk toward a convex mirror. What happens to your image?

3. A convex mirror is held in front of a tree. Is the image of the tree larger or smaller than the tree?

4. A convex mirror has a focal length of $20\ \text{cm}$. Can the image of a bus be $25\ \text{cm}$ behind it?