AQA GCSE Physics Foundation (8463), Foundation tier · Waves › Electromagnetic waves
Practise Lenses. 7 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
How convex and concave lenses form images by refraction, how to draw ray diagrams for them, and how to calculate magnification. GCSE Physics only, not in Combined Science. Expect ray diagrams to complete, image descriptions and magnification calculations (the magnification equation is on the Physics equation sheet).
Key facts
Convex (converging): thicker in the middle; symbol has outward arrowheads
Concave (diverging): thinner in the middle; symbol has inward arrowheads
Principal focus: where parallel rays meet (convex) or appear to come from (concave)
Focal length = distance from the centre of the lens to the principal focus
A ray through the centre of a lens goes straight on
Real image: rays actually meet, can be shown on a screen. Virtual image: rays only appear to come from it
Convex lens: real or virtual image; concave lens: always virtual
magnification = image height ÷ object height (no units; on the equation sheet)
Magnifying glass: object closer to a convex lens than the principal focus
Notes
Lenses and focal length
diagram
A lens forms an image by refracting light.
A convex (converging) lens is thicker in the middle. It brings rays parallel to the principal axis together at the principal focus (F) on the other side.
A concave (diverging) lens is thinner in the middle. It spreads parallel rays out so that they appear to come from the principal focus on the same side as the object.
The focal length is the distance from the centre of the lens to the principal focus. A lens has a principal focus on each side.
In ray diagrams, a convex lens is drawn as a vertical line with outward-pointing arrowheads, and a concave lens as a line with inward-pointing arrowheads.
Convex: parallel rays meet at F. Concave: parallel rays spread out as if from F (dashed).
Drawing ray diagrams
diagram
Draw two rays from the top of the object, using a ruler.
Ray 1, parallel to the principal axis: after a convex lens it passes through F on the far side. After a concave lens it spreads out as if it came from F on the object's side; show this with a dashed line drawn back to F.
Ray 2, through the centre of the lens: it carries on in a straight line.
The top of the image is where the rays cross, or appear to cross.
Object between F and 2F: the image is real, inverted and magnified.
A real image forms where rays actually meet, so it can be shown on a screen. A virtual image is where rays only appear to come from, so it cannot be shown on a screen.
What image you get
Convex lens, object further from the lens than F: the image is real and inverted, on the other side of the lens. It is diminished if the object is more than two focal lengths (2F) away, and magnified if it is between F and 2F.
Convex lens, object closer than F (a magnifying glass): the image is virtual, upright and magnified, on the same side as the object.
Concave lens: the image is always virtual, upright and diminished, on the same side as the object.
Magnification
magnification = image height ÷ object height
Magnification is a ratio, so it has no units. Measure both heights in the same unit (both mm or both cm).
A magnification greater than 1 means the image is bigger than the object; less than 1 means it is smaller.
How to answer each type of question
Calculate magnification or image height
2 to 3 marksGrade 5
Write down magnification = image height ÷ object height.
Put both heights in the same unit.
Substitute, or rearrange to image height = magnification × object height.
Do not give magnification a unit.
Example. A convex lens forms an image of an insect that is 12 mm tall. The image is 4.2 cm tall. Calculate the magnification.
Show the model answerHide the model answer
4.2 cm = 42 mm (1) magnification = 42 ÷ 12 (1) magnification = 3.5 (1)
Don’t lose marks
Giving magnification a unit, such as cm.
Dividing the object height by the image height instead of the other way round.
Using different units for the image height and the object height.
For a concave lens, bending the parallel ray through F on the far side. It must spread out as if it came from F on the object's side.
Not using a ruler, or not extending the rays far enough to cross.
More tips
Memory tricks
Convex bulges out, like the outward arrowheads on its symbol; concave 'caves in', like its inward arrowheads.
With a single lens, real images are always inverted and virtual images are always upright.
Magnification check: if the image is smaller than the object, your answer must be less than 1.
Two rays are enough: 'parallel, then through F' and 'straight through the centre'.
Exam technique
Describe an image with three words: real or virtual, upright or inverted, magnified or diminished (or the same size).
Draw virtual rays and virtual images with dashed lines, and put arrows on real rays.
The magnification equation is on the Physics equation sheet, but you must be able to rearrange it.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 3
Recognise the convex and concave lens symbolsConvex: a line with outward-pointing arrowheads. Concave: a line with inward-pointing arrowheads.
Grade 4
Define principal focus and focal lengthA convex lens brings parallel rays to a focus at the principal focus; the focal length is its distance from the lens.
Grade 5
Calculate magnificationmagnification = image height ÷ object height, with both heights in the same unit; it has no units.
Grade 5
Describe an image in three wordsSay whether it is real or virtual, upright or inverted, and magnified or diminished.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
Lenses form images by refracting light. What is meant by the focal length of a lens?
The distance from the lens to the principal focus.
Where must the stamp be placed for the lens to act as a magnifying glass?
Closer to the lens than the principal focus.
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy5 marks
Lenses form images by refracting light.
(a) How is a concave lens shown in a ray diagram? Tick (✓) one box.[1]
A vertical line with arrowheads pointing inwards at each end
A vertical line with arrowheads pointing outwards at each end
A dashed vertical line
A rectangle
(b) What is meant by the focal length of a lens?[1]
(c) A lens forms an image of an insect. The image is 36 mm tall. The insect is 12 mm tall. Calculate the magnification. Use the equation: \(\text{magnification} = \dfrac{\text{image height}}{\text{object height}}\)[2]
(d) Explain why magnification has no unit.[1]
Show the answer and mark scheme
(a)Answer: A vertical line with arrowheads pointing inwards at each end
(b)Answer: The distance from the lens to the principal focus.
the distance from the lens to the principal focus
(c)Answer: 3
36 ÷ 12
3
(d)Answer: It is a ratio of two heights in the same unit.
it is a ratio of two lengths measured in the same unit (so the units cancel)
Question 2Medium6 marks
Hassan uses a convex lens as a magnifying glass to look at a postage stamp.
(a) Where must the stamp be placed for the lens to act as a magnifying glass?[1]
(b) Give two words that describe the image Hassan sees.[2]
(c) The letters printed on the stamp are 2.5 mm tall. The magnification of the lens is 4.0. Calculate the height of the image of the letters. Use the Physics Equations Sheet.[2]
(d) Explain why the image cannot be projected onto a screen.[1]
Show the answer and mark scheme
(a)Answer: Closer to the lens than the principal focus.
between the lens and the principal focus / closer to the lens than the focal length
(b)Answer: Any two of: virtual, upright, magnified.
virtual
upright / the right way up
magnified / larger than the object
(c)Answer: 10 mm
4.0 = image height ÷ 2.5
10 (mm)
(d)Answer: It is virtual: the rays only appear to come from it.
it is a virtual image: the rays of light do not actually meet there, they only appear to come from the image