Lenses (physics only)

What you'll learn

How lenses form images by refraction.
The difference between convex and concave lenses.
How to draw and interpret GCSE ray diagrams.
How to calculate magnification and investigate it practically.

This is a physics-only part of GCSE Physics, so it appears in separate Physics rather than Combined Science.

The starting idea: lenses refract light

A lens is a transparent object, usually made of glass or plastic, that changes the direction of light passing through it.

The key process is refraction. You have met this earlier in electromagnetic waves: light changes direction when it passes from one material into another, such as from air into glass.

Definition

Refraction

Refraction is the change in direction of a wave when it passes from one medium into another because its speed changes.

A lens forms an image by refracting light from an object. The object is the thing you are looking at; the image is where the light rays meet, or where they appear to have come from.

The principal axis, focus and focal length

Ray diagrams use a few standard reference points.

The principal axis is the straight horizontal line through the centre of the lens. It acts like a “middle line” for drawing rays accurately.

The principal focus is often labelled F. For a convex lens, it is the point where rays that arrive parallel to the principal axis are brought together.

The focal length is the distance from the centre of the lens to the principal focus. It is often labelled $f$ .

Definition

Focal length

The focal length is the distance from the centre of a lens to its principal focus.

Example

Finding focal length from a scale diagram

A ray diagram is drawn to scale. The centre of the lens is at 4.0 cm on the diagram and the principal focus is at 9.5 cm. The diagram scale is 1 cm represents 2 cm in real life.

Find the distance on the diagram from the lens centre to the focus: $\text{ cm}$ .
Convert using the scale: $\text{ cm} \times 2 = 11 \text{ cm}$ .
State the focal length: the lens has a focal length of 11 cm.

Convex lenses: bringing light rays together

A convex lens is thicker in the middle than at the edges. It is also called a converging lens because it brings parallel rays of light together.

In GCSE ray diagrams, a convex lens is represented by a vertical line with outward-pointing arrows at the top and bottom.

For a convex lens, rays parallel to the principal axis are refracted through the principal focus on the far side of the lens.

Ray diagram showing a convex lens bringing parallel rays to a focus and forming a real inverted image

Key Idea

Convex lens takeaway

A convex lens can form either a real image or a virtual image, depending on where the object is placed.

Real and virtual images

A real image is formed where light rays actually meet. Real images can be projected onto a screen.

A virtual image is formed where light rays only appear to have come from. The rays do not actually meet there, so a virtual image cannot be projected onto a screen.

For a convex lens:

If the object is outside the focal length, the image is usually real and inverted.
If the object is closer to the lens than the focal length, the image is virtual, upright and magnified. This is how a magnifying glass works.

Tip

Screen test

If you can catch the image on a screen, it is a real image. If you can only see it by looking through the lens, it is virtual.

Drawing a convex lens ray diagram

To construct a convex lens ray diagram, draw rays from the top of the object.

Use two main rays:

A ray parallel to the principal axis refracts through the far focus.
A ray through the centre of the lens continues straight on.

Where the rays meet is the top of the image. Draw the image arrow from the principal axis to that point.

Common Mistake

Using the wrong meeting point

Do not place the image where one ray crosses the principal axis. The image is found where two rays from the same point on the object meet, or appear to meet.

Concave lenses: spreading light rays out

A concave lens is thinner in the middle than at the edges. It is also called a diverging lens because it spreads light rays out.

In GCSE ray diagrams, a concave lens is represented by a vertical line with inward-pointing arrows at the top and bottom.

For a concave lens, a ray parallel to the principal axis refracts away from the axis. It behaves as if it came from the principal focus on the same side as the object.

Ray diagram showing a concave lens forming a small upright virtual image

Key Idea

Concave lens takeaway

A concave lens always forms a virtual, upright image on the same side of the lens as the object.

Drawing a concave lens ray diagram

Again, draw rays from the top of the object.

Use two main rays:

A ray parallel to the principal axis refracts away from the axis. Extend this refracted ray backwards with a dashed line through the near focus.
A ray through the centre of the lens continues straight on.

The image is where the straight ray meets the dashed backward extension. Because the actual rays do not meet there, the image is virtual.

Example

Identifying an image from a ray diagram

A ray diagram for a concave lens shows the refracted rays spreading apart after the lens. The dashed backward extensions meet on the same side as the object.

Compare the actual rays after the lens: they spread apart, so they do not really meet.
Use the dashed extensions: because only the extensions meet, the image is virtual.
Look at the side and orientation: the image is on the object’s side of the lens and upright, which matches the expected result for a concave lens.

Magnification

Magnification tells you how many times larger or smaller the image is compared with the object.

The equation is:

height\text{magnification} = \frac{\text{image height}}{\text{object height}}

Magnification is a ratio, so it has no units.

Image height and object height must be measured in the same unit, usually millimetres or centimetres.

Example

Calculating magnification

An object is 2.0 cm tall. A convex lens forms an image that is 5.0 cm tall. Calculate the magnification.

Check the units: both heights are in centimetres, so no conversion is needed.
Substitute into the equation:
$magnification=5.02.0\text{magnification} = \frac{5.0}{2.0}$
Calculate the ratio: $magnification=2.5\text{magnification} = 2.5$ .
Interpret the result: the image is 2.5 times taller than the object, and magnification has no units.

Common Mistake

Putting units on magnification

Magnification has no units. Even if the heights are measured in cm or mm, the units cancel because it is image height divided by object height.

Investigating magnification with convex lenses

You may be asked to describe how to investigate the magnification produced by a range of convex lenses.

A typical setup uses:

an illuminated object,
a convex lens in a holder,
a screen,
a metre ruler or optical bench.

Move the lens and screen until a sharp image forms on the screen. Then measure the object height and image height, and calculate magnification.

Experimental setup for investigating magnification using a convex lens, illuminated object, screen and metre ruler

To compare different lenses fairly, keep the object height the same and measure distances carefully from the centre of the lens. Repeat readings to reduce random error.

Tip

Practical accuracy

A sharp image matters. If the screen image is blurry, the measured image height is unreliable, so adjust the lens or screen before measuring.

Convex and concave lenses compared

Both convex and concave lens diagrams use:

a principal axis,
focal points,
rays from the top of the object,
a centre ray that continues straight.

The key difference is what happens to a ray parallel to the principal axis:

A convex lens refracts it towards the far focus.
A concave lens refracts it away from the axis, as if it came from the near focus.

Exam technique

In the exam

Draw ray diagrams with a ruler and label the lens, principal axis, focal points, object and image clearly.
For magnification, make sure image height and object height are in the same unit before dividing.
Decide whether an image is real or virtual by asking: do the actual rays meet, or only the dashed backward extensions?

Self review

Check yourself

What is the difference between a real image and a virtual image?
How does a convex lens affect rays travelling parallel to the principal axis?
Why does magnification have no units?

Lenses (physics only)

What you'll learn

How lenses form images by refraction.
The difference between convex and concave lenses.
How to draw and interpret GCSE ray diagrams.
How to calculate magnification and investigate it practically.

This is a physics-only part of GCSE Physics, so it appears in separate Physics rather than Combined Science.

The starting idea: lenses refract light

A lens is a transparent object, usually made of glass or plastic, that changes the direction of light passing through it.

The key process is refraction. You have met this earlier in electromagnetic waves: light changes direction when it passes from one material into another, such as from air into glass.

Definition

Refraction

Refraction is the change in direction of a wave when it passes from one medium into another because its speed changes.

A lens forms an image by refracting light from an object. The object is the thing you are looking at; the image is where the light rays meet, or where they appear to have come from.

The principal axis, focus and focal length

Ray diagrams use a few standard reference points.

The principal axis is the straight horizontal line through the centre of the lens. It acts like a “middle line” for drawing rays accurately.

The principal focus is often labelled F. For a convex lens, it is the point where rays that arrive parallel to the principal axis are brought together.

The focal length is the distance from the centre of the lens to the principal focus. It is often labelled $f$ .

Definition

Focal length

The focal length is the distance from the centre of a lens to its principal focus.

Example

Finding focal length from a scale diagram

A ray diagram is drawn to scale. The centre of the lens is at 4.0 cm on the diagram and the principal focus is at 9.5 cm. The diagram scale is 1 cm represents 2 cm in real life.

Find the distance on the diagram from the lens centre to the focus: $\text{ cm}$ .
Convert using the scale: $\text{ cm} \times 2 = 11 \text{ cm}$ .
State the focal length: the lens has a focal length of 11 cm.

Convex lenses: bringing light rays together

A convex lens is thicker in the middle than at the edges. It is also called a converging lens because it brings parallel rays of light together.

In GCSE ray diagrams, a convex lens is represented by a vertical line with outward-pointing arrows at the top and bottom.

For a convex lens, rays parallel to the principal axis are refracted through the principal focus on the far side of the lens.

Ray diagram showing a convex lens bringing parallel rays to a focus and forming a real inverted image

Key Idea

Convex lens takeaway

A convex lens can form either a real image or a virtual image, depending on where the object is placed.

Real and virtual images

A real image is formed where light rays actually meet. Real images can be projected onto a screen.

A virtual image is formed where light rays only appear to have come from. The rays do not actually meet there, so a virtual image cannot be projected onto a screen.

For a convex lens:

If the object is outside the focal length, the image is usually real and inverted.
If the object is closer to the lens than the focal length, the image is virtual, upright and magnified. This is how a magnifying glass works.

Tip

Screen test

If you can catch the image on a screen, it is a real image. If you can only see it by looking through the lens, it is virtual.

Drawing a convex lens ray diagram

To construct a convex lens ray diagram, draw rays from the top of the object.

Use two main rays:

A ray parallel to the principal axis refracts through the far focus.
A ray through the centre of the lens continues straight on.

Where the rays meet is the top of the image. Draw the image arrow from the principal axis to that point.

Common Mistake

Using the wrong meeting point

Do not place the image where one ray crosses the principal axis. The image is found where two rays from the same point on the object meet, or appear to meet.

Concave lenses: spreading light rays out

A concave lens is thinner in the middle than at the edges. It is also called a diverging lens because it spreads light rays out.

In GCSE ray diagrams, a concave lens is represented by a vertical line with inward-pointing arrows at the top and bottom.

For a concave lens, a ray parallel to the principal axis refracts away from the axis. It behaves as if it came from the principal focus on the same side as the object.

Ray diagram showing a concave lens forming a small upright virtual image

Key Idea

Concave lens takeaway

A concave lens always forms a virtual, upright image on the same side of the lens as the object.

Drawing a concave lens ray diagram

Again, draw rays from the top of the object.

Use two main rays:

A ray parallel to the principal axis refracts away from the axis. Extend this refracted ray backwards with a dashed line through the near focus.
A ray through the centre of the lens continues straight on.

The image is where the straight ray meets the dashed backward extension. Because the actual rays do not meet there, the image is virtual.

Example

Identifying an image from a ray diagram

A ray diagram for a concave lens shows the refracted rays spreading apart after the lens. The dashed backward extensions meet on the same side as the object.

Compare the actual rays after the lens: they spread apart, so they do not really meet.
Use the dashed extensions: because only the extensions meet, the image is virtual.
Look at the side and orientation: the image is on the object’s side of the lens and upright, which matches the expected result for a concave lens.

Magnification

Magnification tells you how many times larger or smaller the image is compared with the object.

The equation is:

height\text{magnification} = \frac{\text{image height}}{\text{object height}}

Magnification is a ratio, so it has no units.

Image height and object height must be measured in the same unit, usually millimetres or centimetres.

Example

Calculating magnification

An object is 2.0 cm tall. A convex lens forms an image that is 5.0 cm tall. Calculate the magnification.

Check the units: both heights are in centimetres, so no conversion is needed.
Substitute into the equation:
$magnification=5.02.0\text{magnification} = \frac{5.0}{2.0}$
Calculate the ratio: $magnification=2.5\text{magnification} = 2.5$ .
Interpret the result: the image is 2.5 times taller than the object, and magnification has no units.

Common Mistake

Putting units on magnification

Magnification has no units. Even if the heights are measured in cm or mm, the units cancel because it is image height divided by object height.

Investigating magnification with convex lenses

You may be asked to describe how to investigate the magnification produced by a range of convex lenses.

A typical setup uses:

an illuminated object,
a convex lens in a holder,
a screen,
a metre ruler or optical bench.

Move the lens and screen until a sharp image forms on the screen. Then measure the object height and image height, and calculate magnification.

Experimental setup for investigating magnification using a convex lens, illuminated object, screen and metre ruler

To compare different lenses fairly, keep the object height the same and measure distances carefully from the centre of the lens. Repeat readings to reduce random error.

Tip

Practical accuracy

A sharp image matters. If the screen image is blurry, the measured image height is unreliable, so adjust the lens or screen before measuring.

Convex and concave lenses compared

Both convex and concave lens diagrams use:

a principal axis,
focal points,
rays from the top of the object,
a centre ray that continues straight.

The key difference is what happens to a ray parallel to the principal axis:

A convex lens refracts it towards the far focus.
A concave lens refracts it away from the axis, as if it came from the near focus.

Exam technique

In the exam

Draw ray diagrams with a ruler and label the lens, principal axis, focal points, object and image clearly.
For magnification, make sure image height and object height are in the same unit before dividing.
Decide whether an image is real or virtual by asking: do the actual rays meet, or only the dashed backward extensions?

Self review

Check yourself

What is the difference between a real image and a virtual image?
How does a convex lens affect rays travelling parallel to the principal axis?
Why does magnification have no units?

Lenses (physics only)

What you'll learn

The starting idea: lenses refract light

The principal axis, focus and focal length

Convex lenses: bringing light rays together

Real and virtual images

Drawing a convex lens ray diagram

Concave lenses: spreading light rays out

Drawing a concave lens ray diagram

Magnification

Investigating magnification with convex lenses

Convex and concave lenses compared

You've reached the end

Lenses (physics only)

What you'll learn

The starting idea: lenses refract light

The principal axis, focus and focal length

Convex lenses: bringing light rays together

Real and virtual images

Drawing a convex lens ray diagram

Concave lenses: spreading light rays out

Drawing a concave lens ray diagram

Magnification

Investigating magnification with convex lenses

Convex and concave lenses compared

You've reached the end

Lenses (physics only)

What you'll learn

The starting idea: lenses refract light

The principal axis, focus and focal length

Convex lenses: bringing light rays together

Real and virtual images

Drawing a convex lens ray diagram

Concave lenses: spreading light rays out

Drawing a concave lens ray diagram

Magnification

Investigating magnification with convex lenses

Convex and concave lenses compared

You've reached the end

Lenses (physics only) Revision Guide

Lenses (physics only)

What you'll learn

The starting idea: lenses refract light

The principal axis, focus and focal length

Convex lenses: bringing light rays together

Real and virtual images

Drawing a convex lens ray diagram

Concave lenses: spreading light rays out

Drawing a concave lens ray diagram

Magnification

Investigating magnification with convex lenses

Convex and concave lenses compared

You've reached the end

Lenses (physics only) Revision Guide