How converging and diverging lenses bend light, the difference between real and virtual images, how a magnifying glass works, and how to calculate magnification. Separate Physics only.
Objectives
Describe how converging and diverging lenses change the path of parallel rays of light.
State the difference between a real image and a virtual image.
Describe the image made by a magnifying glass.
Calculate magnification using magnification = image height ÷ object height.
Lenses explained
Start here
Have you ever used a magnifying glass to read tiny print, worn glasses, or taken a photo on a phone? All of these use a lens. A lens is a clear curved piece of glass or plastic that bends light, and the bending is what lets it make a picture.
Why does bending light help? Look at a straw in a glass of water and it seems to snap at the surface, because light changes direction where air meets water. A lens uses the same bending, but it does it on purpose and in a careful, curved shape.
A lens can make a picture of an object, and the picture is called an image. The image can be bigger or smaller than the real object, and it can be the right way up or upside down. Whether you can catch it on a screen depends on the lens and how far away the object is.
Think of a football player curling a free kick round a wall. The ball changes direction because of how it is hit, and a lens changes the direction of light because of the shape it is made in. Different shapes give different results, so we need to sort the lenses into two types and learn what each one does to the light that passes through it.
By the end of this lesson you will be able to do three things. First, say what a converging lens and a diverging lens do to rays of light. Second, tell a real image from a virtual image, and describe what a magnifying glass does. Third, use magnification = image height ÷ object height.
A flow of three boxes. An object gives out light, a lens bends the light, and an image is formed.
Converging lenses
A converging lens is thicker in the middle than at the edges. It is also called a convex lens. Think of the shape of a lentil, or of the lens in a magnifying glass, a camera or a pair of reading glasses.
Converging means coming together. When parallel rays of light hit this lens, it bends them all towards one point. Parallel rays are rays that travel side by side in the same direction, like the beams of sunlight from the distant Sun, which arrive almost perfectly side by side.
That meeting point is called the principal focus. The straight line through the middle of the lens is called the axis. The distance from the centre of the lens to the principal focus is the focal length, and a lens has one principal focus on each side, the same distance away, because light can pass through the lens in either direction.
A fatter, rounder lens bends light more strongly, so it brings the rays together closer to the lens and has a shorter focal length. You can test this with two different magnifying glasses and a sunny window. A flatter lens bends light less, so its focal length is longer, and a very flat lens hardly bends the light at all.
This is why a magnifying glass can make a bright dot of sunlight that burns a piece of paper, because all the light that lands on the lens is bent to meet at one spot, and the lenses in cameras and in your own eyes are converging lenses too. Never look at the Sun through a lens, because the focused light can damage your eyes.
A converging lens, thick in the middle, drawn with the two principal foci marked F on either side. An object stands on the left, and rays from the top of the object bend through the lens and meet to form an image on the right that is upside down and smaller.
Diverging lenses
A diverging lens is thinner in the middle than at the edges, and its surfaces curve inwards. It is also called a concave lens. Think of the shape of the inside of a spoon, with the middle pressed in and the rim thicker.
Diverging means spreading apart. Parallel rays that go in are bent outwards, so after the lens they spread out instead of meeting. They never come together on the far side of the lens, however far away you look.
But if you trace the spreading rays backwards, they seem to come from a point on the same side of the lens as the object. That point is the principal focus of a diverging lens. In a ray diagram, such as the one shown here, it is drawn with a dotted line, because the light does not really pass through it, which is a clue that the image will be virtual.
A diverging lens always makes an image that is virtual, upright and smaller than the object. We will explain virtual in the next step, and for now just remember the three words. Some glasses use diverging lenses to help people with short sight, which means that faraway things look blurry.
Here is a quick way to remember the two types. A converging lens is fat in the middle and brings rays together, while a diverging lens is slim in the middle and spreads rays out. If you can picture the shape, you can work out the job. Draw a quick sketch whenever you are unsure.
A diverging lens, thin in the middle, with the principal focus marked F. A ray from the top of the object runs parallel to the axis, then bends outwards after the lens. A dotted line traces that ray back to the principal focus on the object side.
Real and virtual images
An image is the picture of an object that a lens makes. There are two kinds of image, and the difference is where the light really goes. Knowing the difference is a favourite exam question, and it often earns two marks.
A real image is made where light rays actually meet. Because the light is really there, you can catch the image on a screen, like a cinema screen or a sheet of white paper held behind the lens, which is how a film projector shows a picture. The real images made by a single converging lens are upside down, which is why a camera sensor sees the world inverted and the camera flips it for you.
A virtual image is made where the rays only seem to come from. The light is not really there, so you cannot catch it on a screen. You can only see it by looking through the lens, in the same way that you see your face behind a bathroom mirror.
Here is the key test, which you can do in your head. If a screen could show the image, it is real, and if you can only see it by looking into the lens, it is virtual. Real means the light really arrives there, and virtual means it only looks as if it does. Mirrors in your home make virtual images in just the same way.
A converging lens can make either kind, depending on how far away the object is. A diverging lens only ever makes virtual images, which is why you can never use one to project a picture onto a wall. The type of image from a converging lens depends on the object distance, so we only look closely at the magnifying glass case.
The magnifying glass
A magnifying glass is a converging lens used in a special way. You hold the object closer to the lens than the principal focus, which means inside the focal length. That is the key to making it work, and it is why you hold the glass very close to a stamp or a coin.
When you do that, the rays leave the lens still spreading out, so they never meet. Your eye follows them backwards to a point behind the object. The light looks as if it came from that point, and your brain draws the object bigger than it really is.
So the image is virtual. It is also upright, which means the right way up, and magnified, which means bigger than the object. That is exactly what you see when you hold a magnifying glass over a map, a coin or a tiny word in a dictionary, and it is why detectives in old films always carry one.
If you move the object further away than the principal focus, the picture changes. The rays now do meet, and the image becomes real and upside down, just as in a camera or a projector. This is why a magnifying glass only magnifies when it is held close to the thing you are looking at, and why the picture goes blurry and flips over as you pull it away.
Exam tip: if you are asked to describe the image from a magnifying glass, write three words, which are virtual, upright and magnified. Each word is often worth a mark, because examiners award a mark for each correct feature, so do not leave one out, and do not say the image is real.
A flow of four boxes. The object is held closer than the principal focus, the rays spread out after the lens, the eye traces them back, and a virtual, upright, magnified image is seen.
Magnification
Magnification tells you how many times bigger the image is than the object. A magnification of 3 means the image is three times as tall as the object. A magnification of 1 means the image is the same size, and a magnification of 0.5 means the image is only half as tall.
In words: magnification = image height ÷ object height. Put the image height on top, because you are asking how many times the object fits into the image, in the same way that 6 ÷ 2 asks how many 2s fit into 6. If the image is larger, your answer should be more than 1.
Both heights must be in the same unit, such as centimetres. The units then cancel out, so magnification has no unit. Do not write cm or mm after it. If the object is in mm and the image is in cm, convert one of them first.
Here is an example. A beetle is 2 cm long and its image is 10 cm long, so magnification = 10 ÷ 2 = 5, with no unit. The image is five times the size of the beetle, which is why you can see the tiny hairs on its legs.
Use the formula triangle to rearrange the equation, just as you did with speed, distance and time. Put image height on top and magnification and object height along the bottom, then cover the one you want. That gives image height = magnification × object height, and object height = image height ÷ magnification.
A formula triangle for magnification with image height on top and magnification M and object height along the bottom. Cover M to get image divided by object. Cover image to get M times object.
Using the magnification equation
Magnification questions come in three flavours. You may need to find the magnification, the image height or the object height, and the question will always give you the other two. Whichever one it is, write the equation first and then choose how to rearrange it, using the triangle if that helps.
To find the image height, use image height = magnification × object height. A lens with a magnification of 3 and an object 1.2 cm high gives an image 3 × 1.2 = 3.6 cm high. Always check that your answer is bigger than the object when the magnification is more than 1, because that is what the word magnification means.
To find the object height, use object height = image height ÷ magnification. An image 12 cm high with a magnification of 3 means the object is 12 ÷ 3 = 4 cm high. The object is smaller than the image, which is what we expect, and it shows why you divide here rather than multiply.
Look out for different units in one question. Suppose the object is 5 mm high and the image is 2 cm high, which mixes two different units. Change both to the same unit first, because 2 cm is 20 mm, and then the magnification is 20 ÷ 5 = 4. If you forgot, you would get 2 ÷ 5 = 0.4, which is wrong.
A magnification below 1 means the image is smaller than the object. For example, an image 2 cm high from an object 8 cm high has a magnification of 2 ÷ 8 = 0.25. A camera lens often makes a smaller image of a big scene like this, which is how a whole football pitch fits on a tiny sensor, so the magnification there is a small decimal.
Bars comparing an object that is 2 centimetres high with its image that is 6 centimetres high. The image is three times as tall, so the magnification is 3.
Recap
A converging lens, also called a convex lens, is thicker in the middle and brings parallel rays together at the principal focus. A diverging lens is thinner in the middle and spreads parallel rays apart. The focal length is the distance from the lens to the principal focus, and a fatter lens has a shorter focal length.
A real image is formed where the light rays actually meet, and it can be shown on a screen, like a cinema picture. A virtual image is where the rays only seem to come from, so it cannot be shown on a screen. A diverging lens always makes a virtual, upright, smaller image, whatever the object distance.
A magnifying glass is a converging lens with the object closer to the lens than the principal focus. It makes an image that is virtual, upright and magnified. Move the object beyond the focus and the image turns real and upside down, so the position of the object matters.
For magnification, use magnification = image height ÷ object height. Both heights must be in the same unit, and magnification has no unit. A value above 1 means a bigger image, a value of 1 means the same size and a value below 1 means a smaller image.
How this is asked in an exam: you may be given an object height and an image height and told to calculate the magnification, or you may be asked to describe the image from a magnifying glass. Write the equation, substitute the numbers and give the answer with no unit. For a description, use the three key words virtual, upright and magnified.
Key points
A converging lens is thicker in the middle and brings parallel rays to the principal focus.
A diverging lens is thinner in the middle and spreads parallel rays apart.
A real image is where rays meet and can be shown on a screen. A virtual image cannot.
A magnifying glass makes a virtual, upright, magnified image.
magnification = image height ÷ object height, with the same unit for both and no unit in the answer.
Worked examples
Example 1
An object is 2 cm high and its image is 6 cm high. Work out the magnification.
Write the equation: magnification = image height ÷ object height.
Substitute the numbers: 6 ÷ 2.
Work out 3. Magnification has no unit, so the answer is just 3.
Answer: 3
Common slips
Slip: magnification = object height ÷ image height The image height goes on top, because you want to know how many times bigger the image is.
Slip: 6 × 2 = 12 Divide the image height by the object height. Do not multiply them.
Slip: 3 cm Magnification is a ratio, so it has no unit.
Example 2
A lens has a magnification of 4. The object is 1.5 cm high. Work out the height of the image.
Rearrange the equation: image height = magnification × object height.
Substitute the numbers: 4 × 1.5.
Work out 6 cm, and add the unit because this is a height.
Answer: 6 cm
Common slips
Slip: image height = object height ÷ magnification To find the image height you multiply the object height by the magnification.
Slip: 1.5 ÷ 4 = 0.375 That divides, so the answer is much smaller than the object. A magnification of 4 should make it bigger.
Slip: 5.5 cm Do not add 4 and 1.5. Multiply them to get 6 cm.
Example 3
An image is 9 cm high and the magnification is 3. Work out the height of the object.
Rearrange the equation: object height = image height ÷ magnification.
Substitute the numbers: 9 ÷ 3.
Work out 3 cm. The object is smaller than the image, which is what a magnification of 3 gives.
Answer: 3 cm
Common slips
Slip: object height = image height × magnification To find the object height you divide the image height by the magnification.
Slip: 9 × 3 = 27 That would make the object bigger than its image, which cannot be right for a magnification above 1.
Slip: 6 cm 9 ÷ 3 is 3, not 6. Do not subtract.
Questions and answers
Lenses practice questions for GCSE Combined Science Physics. Try each one, then open the answer. Easy questions come first.
Question 1 Easy
Name the type of lens that brings parallel rays of light to a focus.
Show answer
Answer: converging lens
It is thicker in the middle.
This is a converging lens.
Question 2 Easy
Name the type of lens that spreads parallel rays of light apart.
Show answer
Answer: diverging lens
It is thinner in the middle.
This is a diverging lens.
Question 3 Easy
Name the type of image that can be shown on a screen.
Show answer
Answer: real
The rays must actually meet.
This is a real image.
Question 4 Easy
What is the unit of magnification?
Show answer
Answer: no unit
Magnification is a ratio of two heights.
It has no unit.
Question 5 Medium
An object is 3 cm high and its image is 12 cm high. Work out the magnification.
Show answer
Answer: 4
magnification = image height ÷ object height
12 ÷ 3 = 4
Question 6 Medium
An object is 2.5 cm high and the magnification is 4. Work out the height of the image.
Show answer
Answer: 10 cm
image height = magnification × object height
4 × 2.5 = 10 cm
Question 7 Medium
State the difference between a real image and a virtual image.
Show answer
Answer: In a real image the rays actually meet, but in a virtual image they only appear to come from the image.
In a real image the rays meet.
A virtual image is where the rays only seem to come from.
Question 8 Medium
State what a magnifying glass is.
Show answer
Answer: a converging lens
It brings rays together.
It is a converging lens.
Exam-style questions
Longer questions in the style of a written paper, with the marking points. These are Yumio practice questions.
Exam-style question 14 marks
A student uses a converging lens as a magnifying glass to look at a stamp that is 3 cm wide. The image is 12 cm wide.
(a) Work out the magnification. [2 marks]
(b) State two features of the image. [2 marks]
Show answer and marking points
Answer: (a) 4 (b) The image is virtual and upright.
(a) image height ÷ object height (1)
(a) 4 (1)
(b) virtual (1)
(b) upright, or magnified (1)
Exam-style question 24 marks
A converging lens and a diverging lens are used to make images.
(a) Describe what each lens does to parallel rays of light. [2 marks]
(b) State the difference between a real image and a virtual image. [2 marks]
Show answer and marking points
Answer: (a) A converging lens brings parallel rays to the principal focus, and a diverging lens spreads them apart. (b) In a real image the rays meet and it can be shown on a screen, but a virtual image cannot be shown on a screen.
(a) a converging lens brings parallel rays to a focus (1)
(a) a diverging lens spreads the rays apart (1)
(b) a real image is formed where rays meet and can be shown on a screen (1)
(b) a virtual image cannot be shown on a screen (1)
Common mistakes
Saying a diverging lens brings rays to a focus
A diverging lens spreads rays apart. A converging lens is the one that brings them together at the principal focus.
Saying a virtual image can be shown on a screen
Only a real image can be shown on a screen. The rays at a virtual image only seem to meet.
Dividing object height by image height
Magnification is image height ÷ object height, with the image on top.
Giving magnification a unit such as cm
Magnification has no unit. It is a ratio, so the units cancel.
Mixing units, such as mm for the object and cm for the image
Change both heights to the same unit before you divide.
Questions students ask
Is Lenses on the Foundation or Higher tier?
Lenses is on both Foundation and Higher papers for GCSE Combined Science Physics, aimed at around grade 6.
What is a common mistake on Lenses?
Saying a diverging lens brings rays to a focus. A diverging lens spreads rays apart. A converging lens is the one that brings them together at the principal focus.
Where are the answers to the Lenses questions?
Open Show answer under each question on this page. The questions are Yumio practice questions, not past exam questions.