Images formed by lenses

The magnifying glass and the camera

A magnifying glass is a convex lens, and you can use it in two ways. Hold it close to a page, and the letters look large and upright. Hold it far from a page and look through it, and the letters look small and upside down. The image depends on how far the object is from the lens.

Images formed by a convex lens

We draw the principal axis, the lens, and the points $F_1$, $2F_1$, $F_2$ and $2F_2$. Then we draw the object as an arrow on the axis, and we draw two of the three rays from its top.

Object beyond $2F_1$. The image forms between $F_2$ and $2F_2$. It is real, inverted and smaller than the object. This is how a camera works.

Object between $F_1$ and $2F_1$. The image forms beyond $2F_2$. It is real, inverted and larger. This is how a projector forms a large picture on a screen.

Object between $F_1$ and $O$. The rays spread out after the lens, and they do not meet. We trace them back, and the dashed lines meet on the same side as the object. The image is virtual, upright and larger. This is the magnifying glass.

You should find the same pattern as the concave mirror, but a real image of a lens appears on the far side. Far away, the image is small, near $F_2$. Near $F_1$, it runs off the page. Inside $F_1$, it jumps to the object's side.

All the cases of a convex lens in one table

Look at the pattern. It is the same as the pattern of the concave mirror, but a real image of a lens is on the opposite side of the lens from the object. A real image can be caught on a screen. A virtual image cannot.

A worked example

A convex lens has a focal length of $15\ \text{cm}$. A candle stands $40\ \text{cm}$ from it. What is the image like?

1. Find $2F$. $2f = 30\ \text{cm}$.
2. Place the candle. $40\ \text{cm}$ is beyond $2F_1$.
3. Read the table. The image is between $F_2$ and $2F_2$, on the far side: real, inverted and smaller. A screen there shows it.

The image formed by a concave lens

A concave lens makes a parallel ray spread out, so the refracted rays never meet. The image is always:

• virtual,
• upright,
• smaller than the object,
• on the same side as the object, between the lens and $F_1$.

This is true for every position of the object. As the object comes nearer, the image becomes larger, but it never becomes larger than the object.

Uses of lenses

• A magnifying glass, and a watchmaker's lens: a convex lens with the object between $F$ and $O$.
• A camera, and the eye: a convex lens forms a small real inverted image of a distant object on a film or a sensor, or on the retina.
• A projector: an object (a slide) between $F$ and $2F$ gives a large real image on a screen.
• Spectacles: a convex lens for a person who cannot see near objects well, and a concave lens for a person who cannot see far objects well. We study this in the next chapter.

A common mistake

Students often draw a real image on the same side as the object. A real image of a lens is on the other side. A virtual image of a lens is on the same side as the object.

Practise with new numbers

Try it in Python

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

Remember these

• A convex lens forms a real, inverted image when the object is beyond $F$, and a virtual, upright, larger image when the object is between $F$ and $O$.
• A concave lens always forms a virtual, upright and smaller image, on the same side as the object.
• A real image can be shown on a screen. A virtual image cannot.

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 moved from far away toward the focus of a convex lens. What happens to its real image?

2. A convex lens of focal length $10\ \text{cm}$ is $25\ \text{cm}$ from a candle. What is the image like?

3. An object comes closer and closer to a concave lens. What happens to its image?

4. Where is the slide in a projector, compared with the lens, and why is it put in upside down?