Images formed by a concave mirror

One mirror, many images

Hold a spoon far from your face and look into its inside. Your face is upside down. Bring the spoon very close to your eye. Now your face is upright and large. The same mirror gave two different images. The image of a concave mirror depends on the place of the object.

How to draw the image

We draw the principal axis, the mirror and the points $P$, $F$ and $C$. Then:

1. Draw the object as an arrow standing on the axis.
2. From the top of the object, draw ray 1 parallel to the axis. After reflection, it goes through $F$.
3. From the top of the object, draw ray 2 through $F$. After reflection, it goes parallel to the axis.
4. The two reflected rays meet at the top of the image. Draw the image from there to the axis.

Object beyond C

When the object is farther than $C$, the image forms between $F$ and $C$. It is real, inverted and smaller than the object.

Object between C and F

When the object is between $C$ and $F$, the image forms beyond $C$. It is real, inverted and larger than the object.

Object between F and P

When the object is close to the mirror, between $F$ and $P$, the reflected rays spread out, and they do not meet in front of the mirror. We trace them back, and the dashed lines meet behind the mirror. The image is virtual, upright and larger. This is the image that you see in a shaving mirror.

You should find that a far object gives a small image near $F$. As the object comes closer, the image moves out and grows. Close to $F$, the image runs off the page. Inside $F$, it appears behind the mirror, upright and large.

All the cases in one table

Look at the pattern. As the object comes closer from far away, the image moves away from the mirror and gets bigger. At $F$, the reflected rays are parallel, and the image is at infinity. Inside $F$, the image jumps behind the mirror and becomes virtual.

A worked example

A concave mirror has a focal length of $16\ \text{cm}$. A toy stands $40\ \text{cm}$ from it. What is the image like?

1. Find $C$. $R = 2f = 32\ \text{cm}$.
2. Place the toy. $40\ \text{cm}$ is farther than $C$.
3. Read the table. The image is between $F$ and $C$: real, inverted and smaller.

Uses of concave mirrors

• Torches, car headlights and spotlights: the lamp is placed at the focus, so the reflected rays leave as a parallel beam that goes far.
• Shaving mirrors and make-up mirrors: the face is between $F$ and $P$, so we see a larger upright image.
• Dentists: the mirror shows a larger image of a tooth.
• Solar cookers and solar furnaces: the mirror gathers the parallel rays of the Sun at its focus, where the heat is large.

A common mistake

Students often say that a concave mirror always gives a real image. It does not. The image is real when the object is beyond $F$, and virtual when the object is between $F$ and $P$. The test is simple: a real image can be caught on a screen, and a virtual image cannot.

Practise with new numbers

Try it in Python

The program places an object at several distances from a concave mirror, and reads the table for each.

Remember these

• The image in a concave mirror depends on the position of the object.
• Beyond $F$, the image is real and inverted. Between $F$ and $P$, it is virtual, upright and larger.
• Of the three mirrors in this course, only the concave mirror can give a real image.

Check yourself

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

1. An object is $25\ \text{cm}$ from a concave mirror of focal length $10\ \text{cm}$. Between which two points does the image form?

2. An object is $5\ \text{cm}$ from a concave mirror of focal length $10\ \text{cm}$. Is the image real or virtual?

3. Why does a dentist use a concave mirror?

4. A solar cooker uses a concave mirror. Where should the pot go, and why?