Lenses (physics only) — AQA GCSE Physics
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Lenses (physics only) explained
A lens works because light slows down when it enters glass and speeds up when it leaves, so every ray is refracted twice, once at each curved surface.
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Because the surfaces are curved, rays striking different parts of the lens are bent through different amounts, and that is what brings a whole beam together or spreads it apart. A convex, or converging, lens is thicker in the middle and brings parallel rays together. A concave, or diverging, lens is thinner in the middle and spreads parallel rays apart. The image is simply the place where the refracted rays, or their backward projections, meet. A lens never creates light; it only changes the direction of the light already arriving from the object.
In a convex lens, parallel rays of light are brought to a focus at the principal focus.
Send a set of rays parallel to the principal axis into a convex lens and every one of them is refracted so that they all cross at a single point on the axis beyond the lens. That point is the principal focus, and because real light rays actually meet there it is a real focus: place a screen at that point and you see a bright spot. Rays that arrive parallel to each other but at an angle to the axis also converge to a point, but one that lies off the axis. A fatter, more strongly curved lens refracts the rays more, so they meet closer to the lens. Sunlight focused in this way concentrates the energy into a small area, which is why the spot can scorch paper.
The distance from the lens to the principal focus is called the focal length.
The focal length is measured from the centre of the lens to the principal focus, along the principal axis, and it is the single number that says how strongly a lens bends light. A short focal length means a powerful, strongly curved lens that brings rays to a focus quickly; a long focal length means a flatter, weaker lens. A convex lens has a real principal focus on each side, both at the same focal length. You can find the focal length of a convex lens using a distant object such as a window: the rays arriving are effectively parallel, so the sharp image formed on a screen lies at the principal focus and the lens to screen distance is the focal length. The focal length also decides where the image of a nearer object forms.
Ray diagrams are used to show the formation of images by convex and concave lenses.
A lens ray diagram is built from standard construction rays drawn from the top of the object. For a convex lens: a ray parallel to the principal axis is refracted through the principal focus on the far side; a ray through the centre of the lens carries straight on without being deviated; a ray passing through the principal focus on the near side emerges parallel to the axis. Any two of these are enough, and the point where they cross is the top of the image. For a concave lens the parallel ray is refracted so that it appears to come from the principal focus on the same side, and the central ray again passes straight through; the rays are traced backwards as dotted lines to find the virtual image. Use a ruler and mark object and image with arrows.
The image produced by a convex lens can be either real or virtual.
Which kind of image you get depends on where the object is. If the object is further from the lens than the principal focus, the refracted rays actually cross beyond the lens and form a real image: it is inverted, it can be caught on a screen, and it is enlarged when the object lies between F and 2F, the same size at 2F and diminished beyond 2F. If the object is closer to the lens than the principal focus, the refracted rays diverge and never cross, so you trace them back to where they appear to come from; that is a virtual image, upright, enlarged and on the same side of the lens as the object. That is the magnifying glass arrangement. A real image can be projected, a virtual image cannot.
The image produced by a concave lens is always virtual.
A concave lens diverges the light: rays arriving parallel to the principal axis leave the lens spreading apart, as though they had come from a point on the same side as the object. Because they spread rather than converge, they can never cross beyond the lens, so no real image is possible wherever the object is placed. Tracing the emerging rays backwards with dotted lines shows where they appear to come from, and that is the virtual image. For a concave lens it is always upright, always smaller than the object and always on the same side of the lens as the object, lying between the lens and its principal focus. It cannot be formed on a screen because no light actually arrives at that position.
Students should be able to construct ray diagrams to illustrate the similarities and differences between convex and concave lenses.
Both lens types use the same two construction rays, one through the centre that carries straight on and one arriving parallel to the principal axis, and in both cases the image is found where the outgoing rays or their backward projections meet. The difference is what happens to the parallel ray. Through a convex lens it is refracted to pass through the principal focus on the far side, so the rays converge and a real image becomes possible. Through a concave lens it is refracted away from the axis so that it appears to come from the principal focus on the near side, so the rays diverge and only a virtual image is possible. A convex lens can give an inverted or an upright image depending on the object distance; a concave lens always gives an upright, diminished one.
Image height and object height should both be measured in either mm or cm.
Magnification = image height / object height, so it is a ratio of two lengths and has no unit, but only if both heights are measured in the same unit. Measure both in millimetres or both in centimetres; mixing them makes the answer ten times too big or too small. In a diagram question you measure the arrows with a ruler, for example an image 2.0 cm tall and an object 0.8 cm tall, giving a magnification of 2.5. Rearranging lets you find either height, since image height = magnification × object height, so a symbol 1.6 mm tall magnified 3.5 times gives an image height of 5.6 mm. One special case is worth knowing: when the object height is exactly 1 cm, the image height in centimetres is numerically equal to the magnification.
In ray diagrams a convex lens will be represented by: A concave lens will be represented by:
The specification gives standard symbols so that a diagram cannot be misread. A convex, converging lens is drawn as a vertical line with outward pointing arrowheads at both ends, like a double headed arrow. A concave, diverging lens is drawn as a vertical line with inward pointing arrowheads at both ends. In both cases the refraction is shown as a single bend at that line rather than at two curved glass surfaces, which is the standard simplification for GCSE ray diagrams. Draw the principal axis through the centre of the lens at right angles to the line, mark the principal focus F on each side at equal distances, and draw the object as an upright arrow standing on the axis.
Your focus
- Explain how refraction at the surfaces of a lens brings parallel rays to a focus.
- Distinguish a converging from a diverging lens by its shape and by its effect on parallel rays.
- State what is meant by the image in a lens ray diagram.
Show all 27 objectives
- Draw the paths of three rays parallel to the principal axis passing through a convex lens.
- Label the principal focus and the principal axis on a lens diagram.
- Explain why a more strongly curved convex lens has a shorter focal length.
- Measure the focal length of a convex lens from a scale ray diagram.
- Describe a method for finding the focal length of a convex lens using a distant object.
- Explain how the focal length of a lens affects where the image of a given object forms.
- Construct a ray diagram for an object placed beyond 2F from a convex lens and locate the image.
- Complete a ray diagram for a concave lens, using dotted lines to locate the virtual image.
- Describe the three standard construction rays used with a convex lens.
- State the condition on the object distance for a convex lens to form a real image.
- Describe an image fully as real or virtual, upright or inverted, and enlarged or diminished.
- Explain why a magnifying glass must be held closer to the object than its focal length.
- Complete a ray diagram showing how a concave lens forms an image of an object.
- State the three properties of every image formed by a concave lens.
- Explain why a concave lens cannot form an image on a screen.
- Construct side by side ray diagrams for a convex and a concave lens with the object at the same distance.
- Compare the images formed by the two lens types in terms of nature, orientation and size.
- Explain the difference in the path of a ray arriving parallel to the axis for each type of lens.
- Measure image and object heights from a ray diagram and calculate the magnification.
- Rearrange the magnification equation to find an image height from a given magnification.
- Explain why magnification has no unit and why both heights must be measured in the same unit.
- Identify from the symbol on a ray diagram whether a lens is convex or concave, and state what it does to rays arriving parallel to the principal axis.
- Label the principal axis and the principal focus on a lens ray diagram.
- Explain why GCSE ray diagrams show refraction at a single line rather than at two curved surfaces.
Lenses (physics only) exam tips
Marking Points
- one mark for stating that the light is refracted as it enters and as it leaves the lens
- one mark for saying that refraction happens because the light changes speed in the glass
- one mark for identifying a convex lens as converging and a concave lens as diverging
- one mark for defining the image as the point where the refracted rays, or their extensions, meet
- one mark for stating that rays parallel to the principal axis converge after passing through the lens
- one mark for naming the point where they cross as the principal focus
- one mark for saying that the rays actually meet there, so the focus is real
- one mark for linking a more strongly curved lens to a focus closer to the lens
- one mark for measuring the focal length from the centre of the lens to the principal focus
- one mark for using a distant object so that the incoming rays are effectively parallel
- one mark for taking the lens to screen distance for the sharpest image as the focal length
- one mark for linking a shorter focal length to a more strongly curved, more powerful lens
- one mark for a ray through the centre of the lens continuing without deviation
- one mark for a ray parallel to the principal axis refracted correctly at the lens
- one mark for the image drawn in the correct position
- one mark for the image drawn with the correct orientation and size, shown with an arrow
- one mark for stating that the object must be further from the lens than the principal focus for a real image
- one mark for stating that an object closer to the lens than the principal focus gives a virtual image
- one mark for describing a real image as inverted and able to be formed on a screen
- one mark for describing a virtual image as upright and on the same side of the lens as the object
- one mark for the ray through the centre of the lens drawn without deviation
- one mark for the parallel ray drawn diverging as though it came from the principal focus on the same side
- one mark for the image located in the correct position using dotted construction lines
- one mark for the image drawn upright and smaller than the object
- one mark for the undeviated ray through the centre drawn correctly for both lenses
- one mark for the parallel ray refracted through the far principal focus for the convex lens
- one mark for the parallel ray refracted as if from the near principal focus for the concave lens
- one mark for a stated similarity and a stated difference, each supported by the two diagrams
- one mark for both heights read correctly from the diagram, for example image height = 2.0 cm and object height = 0.8 cm
- one mark for a correct substitution into magnification = image height / object height
- one mark for a correct rearrangement when a height is the unknown, such as image height = magnification × object height
- one mark for the final value, with a unit for a height and no unit for a magnification
- one mark for the correct lens symbol, arrowheads outwards for convex and inwards for concave
- one mark for the principal axis drawn through the centre of the lens at right angles to it
- one mark for the principal focus marked at the same distance on both sides of the lens
- one mark for the rays bent at the lens line rather than at two separate curved surfaces
Examiner Tips
- 💡Use the words converging and diverging alongside convex and concave, since both are credited.
- 💡Say where the refraction happens, at the surfaces of the lens, not inside it.
- 💡In a ray diagram, bend the ray at the single lens line, which is the standard GCSE simplification.
- 💡Draw the principal axis first and mark F on both sides at equal distances from the lens.
- 💡Rays parallel to the axis pass through F; that is the first of the standard construction rays.
- 💡Label the principal focus F on the diagram, because the label itself can be the mark.
- 💡State where you measure from and to, because both ends of the measurement can carry marks.
- 💡In a practical question, say that you would repeat the measurement and take a mean.
- 💡Remember the focal length is a property of the lens and does not depend on the object.
- 💡Use a ruler and draw the rays long enough to cross clearly, since short rays cost position marks.
- 💡Two construction rays are enough, but a third is a useful check if the crossing point looks wrong.
- 💡Represent the image with an arrow so that its orientation is unmistakable.
- 💡Mark F and 2F on both sides before deciding what kind of image to expect.
- 💡Describe an image in three parts: real or virtual, upright or inverted, enlarged or diminished.
- 💡If the ray diagram shows the rays diverging after the lens, the image must be virtual.
- 💡For a concave lens the answer to what kind of image is always virtual, upright and diminished.
- 💡Use dotted lines for the projections and a solid arrow for the image itself.
- 💡Check that the image sits between the lens and F, because that is where the construction always places it.
- 💡Draw the two diagrams side by side with the object at the same distance, so the comparison is fair.
- 💡Write the comparison in matched pairs: in the convex lens the rays converge, whereas in the concave lens they diverge.
- 💡Use the correct symbol for each lens, since the symbols themselves carry marks.
- 💡Write the unit next to each measured height before you divide, because that makes a mismatch obvious.
- 💡Magnification has no unit, so leave the answer as a bare number.
- 💡Measure with a ruler to the nearest millimetre and quote the values you used in your working.
- 💡Copy the two symbols into your notes and practise them until the arrow directions are automatic.
- 💡Whatever symbol the question prints, use the same one in your own answer.
- 💡Keep the diagram large, since a small diagram makes the crossing point hard to read and loses position marks.
Common Mistakes
- saying the lens reflects light to form the image
- saying the lens magnifies by making the object bigger, rather than by changing the directions of rays
- showing refraction at only one surface of the lens
- confusing which lens shape converges and which diverges
- drawing the rays crossing at the centre of the lens instead of at the principal focus
- assuming a lens has only one principal focus, when there is one on each side
- drawing the incoming rays already converging before they reach the lens
- saying the principal focus is where the object must be placed
- measuring from the edge or the surface of the lens rather than from its centre
- confusing the focal length with the distance from the lens to the object
- measuring to a blurred image because the screen was not adjusted to the sharpest point
- saying the focal length changes when the object is moved
- bending the ray that passes through the centre of the lens
- drawing the bends at the two curved glass faces instead of at the single lens line, which is the construction the mark scheme expects and makes the angles far harder to draw accurately
- drawing solid lines for the virtual rays behind a concave lens instead of dotted construction lines
- drawing the image the same way up as the object when the construction gives an inverted image
- saying a convex lens always magnifies, when it can also produce a diminished image
- claiming a virtual image can be projected onto a screen
- drawing a real image upright
- deciding the image type from the lens alone without checking the object distance
- drawing the image from a concave lens inverted, by copying the convex lens case
- placing the image beyond the lens on the far side from the object
- using solid lines for the backward projections, which implies light really travels there
- saying the image can be caught on a screen because it looks clear when viewed through the lens
- drawing the same path for the parallel ray through both lenses
- listing similarities and differences without drawing the diagrams the question asked for
- using the convex lens symbol for both diagrams
- giving a difference that is only about the shape of the glass, with no effect on the rays
- measuring the object in millimetres and the image in centimetres, so the magnification is out by a factor of ten
- giving the magnification a unit such as cm or times
- inverting the ratio by dividing object height by image height
- measuring the object and image arrows inconsistently, including the arrow head on one but not the other
- drawing the lens as a shaped piece of glass and then refracting at both curved surfaces
- using outward pointing arrowheads for a concave lens
- marking F at different distances on the two sides of the lens
- drawing the object arrow off the principal axis, so the construction rays no longer work