Ray Diagrams
Light, Sound and Waves

Introduction to rays and images

for 14-16

Rays of light can be observed in many different ways. In these experiments, students see light rays reflect and bend, produce shadows and images.

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Shadows and rays on a screen

Ray Diagrams
Light, Sound and Waves

Shadows and rays on a screen

Practical Activity for 14-16

Demonstration

Shadows form on a screen when objects interrupt the light from a lamp.

Apparatus and Materials

  • Compact light source (quartz iodine lamp) or 100 W 12 V lamp
  • L.T. variable voltage supply (12 V 8 A)
  • Retort stand and boss
  • White screen or blank wall
  • Card with slot

Health & Safety and Technical Notes

Be aware that compact light sources using tungsten-halogen lamps without filters are significant sources of UV. Ensure that no-one can look directly at the lamps.

Read our standard health & safety guidance


If you don't have a compact light source use a 48 W 12 V lamp.

Procedure

  1. Set up the compact light source in front of the screen or wall, preferably with the room darkened.
  2. Put various obstacles between the source and the screen so that shadows are seen. A card with a slot will give straight shadows on the wall. The shadows will be sharpest when the edges of the card and the slot are parallel to the lamp filament.
  3. Move the light source closer to the screen so that a wide beam of illumination falls across it.
  4. Bring up a card with a slit in it as illustrated to show how a ray of light can be made.
  5. Trinity College, Cambridge

Teaching Notes

  • The demonstration in 2 shows what happens when a lamp throws light onto an object and a shadow falls onto a screen.
  • You can vary the relative distances between the lamp and object, and the screen and object, to show the umbra and penumbra in the shadow. You might want to mention eclipses.
  • The narrow slit placed in the beam in 4 shows how a ray of light can be produced. The ray of light appears to travel in a straight line.

This experiment was safety-tested in January 2007

Up next

Ray of light in water

Ray Diagrams
Light, Sound and Waves

Ray of light in water

Practical Activity for 14-16

Demonstration

A light ray can be seen in water coloured with fluorescein.

Apparatus and Materials

  • Light source, compact (100 W 12 V)
  • L.T. variable voltage supply (12 V 8 A)
  • Retort stand and boss
  • Tank, large rectangular transparent
  • Converging lens
  • Lens holder
  • Fluorescein solution
  • Small screen (100 mm x 100 mm approx) with 10 to 20 mm diameter hole

Health & Safety and Technical Notes

Be aware that compact light sources using tungsten-halogen lamps without filters are significant sources of UV. Ensure that no-one can look directly at the lamps.

Read our standard health & safety guidance


The compact light source will ideally consist of a 12 V, 100 W tungsten-halogen lamp in a suitable housing.

Fluorescein does not dissolve easily. Dissolve it first in a little alcohol, then dilute with water.

Fluorescein is best used in concentrations between 5 x 10 -4 g/litre and 5 x 10 -3 g/litre. These are most easily obtained by dissolving 1 g of fluorescein in 1 litre of water to make a stock solution. Between 0.5 ml and 5 ml of this stock solution is then used to each litre of water. Lower concentrations give very good contrast between the light and dark parts of the water. Higher concentrations give brighter rays and are probably better for long-distance viewing.

If fluorescein is not available, a few drops of milk will show up the beam by scattering the light.

Procedure

  1. Fill the tank with water containing a little fluorescein (see above). Place a converging lens a suitable distance in front of the hole to produce a parallel beam of light.
  2. Place the screen containing the hole after the lens, to limit the beam to a narrow horizontal pencil. Direct this pencil of light through one end of the tank.
  3. Look at the pencil of light through the front of the tank. If you scatter a little smoke or chalk dust in the air, it makes the pencil of light visible in the air before it enters the tank and after it leaves.
  4. Students can also look through the end of the tank, looking along the ray to see that it is straight.

Teaching Notes

The purpose of this introductory demonstration is simply to show that light propagates along straight paths as rays.

This experiment was safety-tested in December 2004

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Curved ray of light

Ray Diagrams
Light, Sound and Waves

Curved ray of light

Practical Activity for 14-16

Demonstration

A ray of light bends as it passes through a region of changing refractive index.

Apparatus and Materials

  • Light source, compact (100 W 12 V)
  • L.T. variable voltage supply (12 V 8 A)
  • Retort stand and boss
  • Tank, large rectangular transparent
  • Converging lens
  • Small screen (100 mm x 100 mm approx) with 10 to 20 mm diameter hole
  • Lens holder
  • Fluorescein solution
  • Class 2 laser source (optional)

Health & Safety and Technical Notes

Be aware that compact light sources using tungsten-halogen lamps without filters are significant sources of UV. Ensure that no-one can look directly at the lamp.

Although a class 2 laser is safe no-one should stare down the beam. If a laser is used, the tank should be viewed only from the front. (It is still worth doing with a laser as well as with a compact light source to show the laser beam being bent.)

Read our standard health & safety guidance


Preparing the tank

  • Some hours before the demonstration, make up a very concentrated solution of common salt. Filter it to remove any cloudiness. Add a little fluorescein to colour it. See Ray of light in water to find out how to make fluorescein solution.
  • Fill the tank about half full with plain water, coloured with enough fluorescein to match the colour of the brine.
  • When the plain water has settled down to rest, introduce the salt solution very gently at the bottom. This can be done by pouring it in through a funnel fitted with a rubber tube (and a clip), extending to the bottom of the tank. As the brine is poured in, it will take its place under the water without mixing too much. Since some mixing is necessary, you don't need to pour very carefully.
  • Let the tank stand for some hours. This is so that diffusion creates a region about one or two centimetres thick, in which the refractive index changes from that of brine to that of water. You may need to increase the mixing provided by diffusion simply by stirring the boundary region gently with a finger.
  • Prepare the tank where you will carry out the demonstration. Otherwise, the liquid density gradient will be disturbed by moving the tank.

Procedure

  1. Place the screen containing the hole after the lens, to limit the beam to a narrow horizontal pencil. Direct this pencil of light through one end of the tank, horizontally at the mixing layer. You will need to tilt the ray from the horizontal and move it up and down until the best effect is observed.
  2. Ask students to look at the ray from the front of the tank and then from the end of the tank along the ray.
  3. Stir the water and brine together so that they mix. The rays become straight, whichever way you look at them.

Teaching Notes

  • If students look from the front of the tank they will see that the ray is bent. This is where the ray passes through the region of changing refractive index. But if they look along the ray, through the end of the tank, they will see something quite different, their line of vision follows the same path as the ray in the water, and the ray appears straight.
  • This demonstration models the refraction of light in the Earth's atmosphere. The density of air is greatest near the Earth's surface and falls steadily with altitude.
  • This demonstration is best if it is shown at a different time from:

    Ray of light in water


This experiment was safety-tested in August 2006

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Reflecting a ray of light and a rubber ball

Reflection
Light, Sound and Waves

Reflecting a ray of light and a rubber ball

Practical Activity for 14-16

Demonstration

Comparing the paths of a reflected ray of light and a rubber ball.

Apparatus and Materials

  • Light source, compact (100 W 12 V)
  • L.T. variable voltage supply (12 V 8 A)
  • White screen (500 mm x 300 mm approx)
  • Card with slit (5 mm wide approx)
  • Retort stand and boss
  • Plane mirror
  • Rubber ball

Health & Safety and Technical Notes

Be aware that compact light sources using tungsten-halogen lamps without filters are significant sources of UV. Ensure that no-one can look directly at the lamp.

Read our standard health & safety guidance


Procedure

  1. Set up the compact light source with the card and slit in front of it, so that a thick ray of light splashes across the vertical white screen.
  2. Catch the ray with a piece of plane mirror held in the hand and reflect it across the screen.
  3. Bounce the rubber ball against a hard wall or floor to show its reflection.

Teaching Notes

  • This demonstration introduces the idea of reflection. It is not intended for careful measurements, but students should see some connection between the angles.
  • Make sure that students observe the similarity between the path of the ray of light, and the path of the ball.
  • You could ask the question 'What is light made of... bullets?'. If students have seen waves being reflected in a ripple tank, they might also give waves as an answer.

This experiment was safety-tested in August 2006

Up next

Real and virtual images in a smoke box

Ray Diagrams
Light, Sound and Waves

Real and virtual images in a smoke box

Practical Activity for 14-16

Demonstration

Shows rays forming an image in the smoke with a lens and a mirror, as well as the effects of chromatic and spherical aberration.

Apparatus and Materials

  • Smoke generator or bee-smoker
  • Corrugated cardboard to burn
  • Plano-convex lens, large (100 mm approx)
  • Concave mirror, large
  • Lens holder
  • Aluminium screen with one large hole (50 mm approx)
  • Aluminium screen with 50 mm circle of holes
  • Aluminium screen with 75 mm circle of holes
  • Light source, compact (100 W 12 V)
  • L.T. variable voltage supply (12 V 8 A)
  • Retort stand and boss
  • Smoke box


Health & Safety and Technical Notes

Be aware that compact light sources using tungsten-halogen lamps without filters are significant sources of UV. Ensure that no-one can look directly at the lamp.

The method of making smoke with a bee-smoker is safe. Do not be tempted to generate smoke with chemicals.

Read our standard health & safety guidance


  • You can use the smoke box for a number of demonstrations. If you cannot buy one, construction details are given in the Smoke box apparatus listed above.
  • Good smoke can be made by rolling up corrugated cardboard, lighting it and inserting the lit end into the bottom of a bee-smoker. Take care not to extinguish the flame too quickly by pushing the bellows too hard to begin with.
  • The plano-convex lens should be of condenser quality, about 100 mm in diameter, 150 mm focal length. A suitable lens is obtainable from Knight Optical, part number LPC15050:

    Knight Optical (UK) Ltd


  • The large concave mirror can be one of the cheap plastic mirrors often supplied in multiple packs, although these only have a focal length of about 40 mm.
  • The aluminium screen has a series of small holes drilled in a circle of about 50 mm diameter. This produces a cone of rays when a light is shone at it. A second screen with the holes in a circle of about 75 mm is useful too.
  • The laboratory needs to be quite dark for the smoke to be seen clearly.
  • Smoke will slowly escape from the box and will need replacing regularly, but there really is no need for coughing fits from disruptive students! So warn them!
  • Clean the lens and mirror before putting them away.

Procedure

  1. Put the lens inside the box, about 100 mm from the end, with its convex side towards the lamp. This will reduce aberration.
  2. Attach the aluminium sheet with holes to the end of the box.
  3. Light a piece of corrugated cardboard with a match. When it is burning, insert it in the smoke generator. Insert the generator through the opening in the back of the smoke box. Several strokes of a bee smoker should fill the box.
  4. Place the compact light source about 1/2 a metre from the lens, outside the smoke box.
  5. Bring the lamp nearer to the lens and observe how the image changes.
  6. Take away the screen with holes and replace it with the screen with one large hole. This is to show the effect of the lens on the beam of light and, less vividly, the dark shadow produced by the lens. Observe the aberrations.
  7. Remove the screen with the large hole and insert the screen with the smallest circle of holes. Move the lens close to the entrance window, this time with the convex side of the lens facing away from the lamp, to minimize aberration. Place the lamp near the window. To show rays diverging from a virtual image, the lamp must be at most 120 mm from the lens. Fill the box with smoke as before.
  8. Remove the lens from the box. Return the lamp to its original position about half a metre from the front of the box, with the aluminium screen with the 50 mm circle of holes in position. Place the concave mirror in the box and fill it with smoke. Direct a fan of rays at the mirror.

Teaching Notes

  • The lamp and the lens should be placed so that the rays cover the full aperture of the lens. Rays which fall outside the lens aperture carry on in a straight line, providing a useful lesson about rays of light.
  • When you first inject smoke into the box it will swirl around inside. When it settles, a beautiful 3D fan of rays will be revealed. These rays are bent by the lens to form an image in space, with the rays passing straight through the image. The smoke in the smoke box scatters some of the light so that the rays can be seen.
  • Students will have to walk round the box looking at the rays from the side and near end-on to get the best effect. (Although rays can be seen best by observers looking upstream towards the light source, it is unwise to do this because of the UV content.)
  • When the lamp is brought nearer to the lens, in 5, the image moves further away.
  • Here are two kinds of lens defect, or aberration:
    • The screen with a large hole will produce a bright cone, with coloured edges. The red rays are brought to a different focus from the blue ones. This is called chromatic aberration.
    • The image will be fuzzy because outer rays of the cone will not be brought to the same focus as more paraxial rays. This is called spherical aberration.
  • When the lens and the light source are close together, as in 7, the rays splay out so strongly that the lens cannot bend them enough to form a real image. However, it does bend them so that the rays seem to come from a virtual image behind the lamp. This is how a magnifying glass behaves.
  • Using a concave mirror as in 8, is another way to produce a real image. This time there is no chromatic aberration. Point out that this gives reflecting telescopes an important advantage over refracting telescopes.
  • The smoke box can be seen as a pinhole camera, cut along its length. You can see what the lens is doing to the rays of light. The holes in the screen represent the holes in the pinhole camera.

This experiment was safety-tested in December 2006

Up next

How images form

Ray Diagrams
Light, Sound and Waves

How images form

Practical Activity for 14-16

Demonstration

Investigating the formation of real images.

Apparatus and Materials

  • Light source, compact (100 W 12 V)
  • L.T. variable voltage supply (12 V 8 A)
  • Aluminium screen with 50 mm circle of holes
  • Plano-convex lens, large
  • Retort stands, bosses and clamps, 3
  • Screen, white
  • Greaseproof paper

Health & Safety and Technical Notes

Be aware that compact light sources using tungsten-halogen lamps without filters are significant sources of UV. Ensure that no-one can look directly at the lamp.

Read our standard health & safety guidance


The plano-convex lens should be of condenser quality, about 100 mm in diameter, 150 mm focal length. A suitable lens is obtainable from Knight Optical, part number LPC15050.

The aluminium screen has a series of small holes drilled in a circle of about 50 mm diameter, so that a cone of rays is produced when a light is shone at it.

Procedure

  1. Position the lens about half a metre from the lamp, with its convex side towards the lamp. This reduces aberration. Hold the aluminium screen with holes between the two, and about 100 mm from the lens. Position the lamp, aluminium screen and lens so that the lens forms a real image about half a metre beyond the lens on the screen.
  2. This is the same arrangement as for

    Real and virtual images in a smoke box


    but without the box or smoke.
  3. Adjust the positions so that the pencils of light from the outer holes in the screen meet the lens at places near its edge.
  4. Show that there are rays proceeding from the aluminium screen to the lens. Do this by moving a piece of greaseproof paper to catch those rays in the space between the screen and the lens.
  5. Ask what happens to the rays beyond the lens. Bring students close enough to see what does happen. Do this by waving a sheet of greaseproof paper in the space between the lens and the image, and on beyond.

Teaching Notes

  • Although the lens bends pencils of light to pass through the image point, neither rays nor image are visible to an audience in a dark room without smoke to scatter light.
  • The lens forms a real image some distance beyond the lens.
  • If the plate is removed, an image of the lamp will be seen clearly on the paper screen.
  • The lens is stronger for blue light than red light, and so coloured images of the lamp will be seen at different distances from the lens.

This experiment was safety-tested in August 2006

Up next

Image formation with a lens

Ray Diagrams
Light, Sound and Waves

Image formation with a lens

Practical Activity for 14-16

Demonstration

A set of experiments to introduce real and virtual images formed by a convex lens.

Apparatus and Materials

  • Lens (+7D or 150 mm focal length)
  • Sheet of plain white paper
  • Greaseproof paper, small pieces
  • Floodlights (optional)

Health & Safety and Technical Notes

If the Sun is visible from the laboratory windows, it is essential for the teacher to remind students that looking at the Sun through a lens will cause blindness.

Read our standard health & safety guidance


In the following description, the source of light is referred to as a window. In some cases an electric lamp may be better, as it can be used in a room that is at least half dark. A carbon filament lamp and mounted lampholder are suitable.

Procedure

  1. Lenses forming real images
    • Face away from the window, holding a sheet of paper at arm's length. Hold the lens in front of the paper and move it to and from the paper (towards you and back towards the paper) until you see an image of the window on the paper.
  2. Real image with and without screen
    • Hold a lens at arm's length towards the window. Hold a piece of greaseproof paper in the other hand and find the place between the lens and your head where there is a clear image of the window on the paper. You are looking at that image through the paper. Your eyes should be focused on the paper itself.
    • Remove the paper and look at the image in space. If you cannot find the image put the paper back and repeat the process. It may be helpful to catch half the image on the edge of the paper and the other half in space. Concentrate on the image on the paper and slide the paper away.
  3. Looking at the real image of a brightly illuminated face
    • Darken the room and illuminate the face of a student brilliantly with floodlights. Form an image of the model's face and notice how the picture moves farther from the lens and grows in size as you move the lens nearer to the model.
    • Try this with a piece of thin paper to catch the image, and without it.
  4. Quick rough estimate of focal length
    • Hold the lens so that it forms an image of a distant window or lamp on a sheet of paper or a wall and measure (roughly) the distance from lens to image.
  5. Virtual image
    • Hold the lens close to your eye and use it as a magnifying glass to look at your thumb.

Teaching Notes

  • In part 1 this works best if the laboratory is fairly dark and a blind is opened onto a bright window so that a bright image is produced. (If the Sun is visible from the laboratory windows, it is essential for you to remind students that looking at the Sun through a lens will cause blindness.) The brighter the image, the more colourful it will look. This always surprises some students, before they even notice that the image is upside down. Begin with a +7D lens and then use lenses of different powers. Note the distance between the lens and the screen.
  • Many students will need help to do part 2, but the time spent helping them will be worth it. Remind them that they will not see an object clearly when it is very close to their face: they must be a considerable distance from it. If they cannot find the image, put the paper back and repeat the process. Give help by suggesting to them that the image is located in space, just where the paper was. To see it, their eye must be focused at that place.
    • A real image can be caught on a screen, but the screen isn't necessary for its production. This is just like an image on the film in a camera; the image is upside down and smaller than the object.
    • You might introduce this to students by asking questions: "What will happen if you take the greaseproof paper away? Will the image still be there?"
    • Remind students not to put their eye at the greaseproof paper. Their eyes should be at least a distance from the paper, as if they were viewing a digital camera.
    • You could ask the students: "When you face the window and look through the lens, the image appears to be on the lens. But is it?"
    • When you catch the image on greaseproof paper and then move the paper away, sideways, you show that the image is in space between the lens and your eye. The screen is not necessary.
  • In part 3, as the lens is moved towards the object being viewed, the image moves back and grows in size. You might summarize this for students like this:
    • "You see a thing by receiving rays which come straight to your eye from each point on that thing. A lens bends the rays that come from a bright point, and makes all of them pass through another bright point which we call the image. You see that image by receiving rays coming from it to your eye."
    • "That is what a camera lens does. It makes an image of the thing you want to photograph, and the photographic film or CCD element is put just at the image position."
    • The image sensor in a digital camera is a 'charge-coupled device' but it is not appropriate to explain this term."
  • The focal length of a lens is one way of classifying lenses. The focal length is the distance between the focal point and the lens when viewing a distant object (infinity). The focal length is a constant for the lens.
    • The power of the lens is 1/ f. (1/ f gives the change in wave curvature imprinted on any spherical wave by a lens.) The stronger the lens, the shorter is the focal length.
    • Convex lenses have a positive power, and concave lenses a negative power.
    • (The word, focus, comes from the Greek word meaning hearth. When a lens forms an image of the Sun, then it will burn a piece of paper placed at the focus.)
  • All beginners find the idea of a virtual image more difficult than that of a real image, see part 5. Some are helped by being shown a plane mirror forming a virtual image. This is not always as helpful as teachers hope since, to a beginner, the plane mirror acts in quite a different way from a transparent lens. So offer a plane mirror demonstration only as a tentative help to those who are having great difficulty. You might use the following instruction:
    • "Hold the lens close to your eye, with your thumb at the right place for looking at it. Whip the lens away and see whether you can see your thumb. Without the lens your thumb is too close for you to look at and see comfortably at that distance."
    • "Now put the lens back. You can see your thumb comfortably and it looks big. Where must the image be? What is the range of places for objects that you can see comfortably? It's from about 25 cm in front of you to right out away at infinity. Where must that image of your thumb be when you can see it comfortably with this magnifying glass? The image you are looking at must be out in front of you, like anything else your eyes can see comfortably. It must be on the same side of the lens as your thumb, but further away."
    • "We call that a virtual image, one that the rays of light seem to come from, but don't actually pass through. You cannot catch that image on a piece of paper."
  • This set of experiments reveals some facts about convex lenses and the links between object and image distance.
    • When the object moves towards the lens, the image moves away from the lens on the other side of the lens.
    • When the object is at infinity, the image is at the focus.
    • When the object is at the focus, then the image is at infinity.
    • When the object is between the focus and the lens, then the image becomes virtual and returns behind the lens on the same side as the object.
    • The magnification changes and increases as the object distance is reduced.
    • When the object is at 2 f then the image is at 2 f on the other side of the lens and there is no magnification.

This experiment was safety-tested in January 2007

Up next

The lens formula

Ray Diagrams
Light, Sound and Waves

The lens formula

Practical Activity for 14-16

Class Practical

Making rough measurements to check the validity of a lens formula.

Apparatus and Materials

  • Telescope mount
  • Convex lens
  • Retort stands and bosses, 2
  • Lamp with holder
  • Power supply, low voltage, 6 V
  • Metre rule
  • Screen, white
  • Calculator

Health & Safety and Technical Notes

Read our standard health & safety guidance


The lamp, if run at 12 volts, is too bright for viewing directly when looking at virtual images. It works well operated at 6 volts instead of 12.

Alternatively, you can use a pea-lamp, i.e. a round MES bulb.

If you have a telescope mount it makes a useful and cheap optical bench for these measurements.

Procedure

  1. Tell students that for a simple lens the object distance, u, and image distance, v, are known to be related. Give them the appropriate formula for the convention you are using:
  2. 1/ u + 1/ v = 1/ f for 'real is positive'
  3. or 1/ u + 1/ f = 1/ v for 'Cartesian'
  4. Tell students that the constant 1/ f is a property of lenses. It can be predicted by using geometry from knowledge of the way in which rays of light are bent at each surface of a lens. Or, 1/ f can be predicted from the way in which a whole lens always bends a fan of rays to pass through an image point. Or, 1/ f could be extracted from a large number of experimental measurements.
  5. Set up the lamp and screen on the axis of the lens with the lamp. Move them to obtain a clear image of the lamp filament on the screen. Measure v and u.
  6. Real is positive: Calculate the value of 1/ u + 1/ v (both positive). Repeat for several different values of u. Does this always give about the same value?
  7. Cartesian: Give students the focal length of the lens being used. If you add the power of the lens 1/ f (positive) to 1/ u (which is negative), does it always give you 1/ v (positive)? Repeat for several different values of u.
  8. Move the lamp or a piece of paper with a vertical arrow on it much closer to the lens so that a real image cannot be formed. This should be at an object distance of about half the focal length of the lens. Look at the virtual image of the lamp through the lens. Place a retort stand behind the lamp and move it till the virtual image of the lamp appears to be near it. (See the second Teaching note)
  9. Measure u and v (now a negative value) and try them in the same formula. Repeat for one or two different lamp positions.

Teaching Notes

  • The aim of this experiment is to provide an amusing game that will give students practice in locating virtual images. It is not to bring out the formula and make it important in the teaching. Virtual images cannot be caught on a screen.
  • The catcher for the virtual image in part 8 may be a tall retort stand seen above the lens. It is moved until the virtual image seen by one eye, and the stand seen by the other eye, seem to be in focus together, and remain together as the observer wags his/her head.
  • Use a calculator to calculate the reciprocal values. Putting the values into the lens equation (real is positive) do not appear to fit until the image distance is given a negative sign.

This experiment was safety-tested in January 2007

Up next

Teaching ray optics

Reflection
Light Sound and Waves

Teaching ray optics

Teaching Guidance for 14-16

At introductory level, simple experiments can help students to realize that light travels in straight lines and that an object is seen when light from the object enters the eye. A lens bends light rays so that the rays pass through an image point and we think we see the object at that point.

Treated as open-ended experiments they show students the way in which light behaves with real lenses in optical instruments.

Photograph courtesty of Jim Jardine

Most of the experiments described on this website are suitable for intermediate level courses. After completing them, students should be able to draw a diagram of light rays (not formal ray construction diagrams) showing the following.

  • Rays travel out from an object point in all directions, going fainter as they go farther.
  • All rays from a remote object point pass through an image point.
  • Rays from a remote object point which pass through a lens and proceed to a real image point after the lens, continue straight on through that point.
  • Rays from an object point which pass through a lens forming a virtual image emerge along lines that appear to come straight from the image point.
  • Every ray aimed at a central point in a lens (called the optical centre) passes through undeviated.

The real behaviour of rays falls short of the ideal of passing through images exactly. Students will see this and learn a little about correcting for that aberration.

The ray optics equipment suggested in these experiments looks simple, but some practical skill is needed to get the best out of it. Teaching notes provided with each experiment will help you ask the right questions of students struggling to get results.

You will be better prepared for student questions if you try out the experiments carefully beforehand. It is also advisable to read traditional textbooks that go beyond what students need to know for examination purposes. For example, knowing that the minimum distance between object and image is four times the focal length of a converging lens will enable a teacher to choose a lens that suits the length of a demonstration bench.

A well-organized cafeteria of equipment, under teacher control, will encourage students to do their own experimenting. In this way, extension work for faster students can be encouraged.

At intermediate and advanced level, ripple tanks can be brought in when needed, to show reflection or refraction for example. Wave theory predicts that all parts of a wavefront starting from a small light source arrive in phase at the image. This requires all paths from the object to take the same time.

Up next

The longitudinal lens formula and sign conventions

Ray Diagrams
Light Sound and Waves

The longitudinal lens formula and sign conventions

Teaching Guidance for 14-16

The simple lens formula for thin lenses is included in some advanced level physics courses, though it is rarely used by contemporary optical designers. It provides a source of examination questions and a wrangle about sign conventions. Conventionally, u is the distance from lens to object, v is the distance from lens to image, and f is the focal length of the lens.

If treated lightly, the formula can be put to good use as an encouragement to students to practise placing virtual images. Nearly everyone uses an optical instrument sometimes. In most optical instruments (telescope, microscope, magnifying glass, spectrometer) the observer looks at a virtual image.

The important thing in the argument about conventions is to choose one convention and stick to it. Advantages and disadvantages of the two common conventions are discussed below.

The Cartesian convention

The Cartesian convention emphasizes the point of view which looks at a lens as changing the curvature of wave fronts going through it. One reason to do this is that it makes good sense of the reciprocal quantities in:

1/ v =1/ u +1/ f

Thinking of a lens as adding curvature, the natural formulation is:

curvature after = curvature before + curvature added

This convention also expresses the fact that the effective power of two thin lenses in contact is found by adding their powers.

In both conventions, diverging lenses have negative powers and converging lenses have positive powers. In the Cartesian system, it is advisable not to restrict the unit dioptre to lens powers alone, but extend it to 1/ v and 1/ u . Indeed, this must be correct if the equation is to have consistent units. Opticians always measure lens powers in dioptres, and so the unit itself is more than respectable.

It is better to express the lens equation in the form above rather than as:

1/ v – 1/ u = 1/ f

where it may be less easy to recall which term is subtracted (though reading this as 'change in curvature = curvature provided by the lens' is quite natural).

In the Cartesian convention, distances to the right are positive and distances to the left are negative, just the same as for cartesian graphs. For a converging lens forming a real image, u is negative and v is positive.

The real is positive convention

1/ u + 1/ v = 1/ f

In the real is positive, the symbols are taken at face value and the fact that these reciprocals are related receives no attention. The sign is taken as positive for a real object or image distance, and negative for a virtual object or image distance.

Advantages: The merit of this convention is that it makes the lens equation simple and easy to remember. Double negatives, which can confuse students, do not arise in as many cases as with the Cartesian system.

Disadvantages: The real is positive sign convention is not used at all in professional work in optics, nor in ray tracing software which is readily available, and it obscures what is going on underneath. Some students get confused between the sign of (-1/ u ) and the sign of u itself.

Thanks to Dave Martindale for pointing out an error on this page, now corrected. Editor

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