With a camera, rays of light come straight from each point on a bright filament, brightly lighted face, or whatever the object is that you are photographing.

The picture on the back of a pinhole camera is made by those rays which go straight through the pinhole. The front wall of the camera stops all other rays.

The sketch shows rays of light from just two specimen points on a lamp filament contributing to the picture at the back. Each point on an object provides rays for a little spot in the picture at the back, a spot slightly larger than the pinhole. With a small enough pinhole, you get a fairly sharp picture.

With a large pinhole, you no longer get a point-for-point copy of the object. You get a patch-for-point copy, rather a fuzzy picture.

When there are several pinholes, each lets through rays of light from every part of the object. So each pinhole leads to a whole picture of the object.

Look at the diagram and imagine what the lens does.

For light starting from a single point, the lens seems to collect up the rays that go through different pinholes. It bends them so that they all run together through a point. That point is called the image.

To know what the lens really does, you must let a lens receive many rays of light and see how it deals with them.

The ray box is a useful and convenient piece of apparatus for demonstrating optical phenomena, but be aware of its limitations. When using ray boxes, you need to make sure that students do not make invalid assumptions. Take care to bring out the correct physics. Here are some suggestions.

Ray streaks

The pattern of light emerging from the comb (or slits) in front of a ray box (or simple lamp) is often treated as if it consists of discrete rays, but it does not. What you see on the paper fixed to the bench are streaks of light, each emanating from a range of points along the extended object of the lamp filament. A succession of beams constitutes a line across the surface on the bench. This is more correctly described as a shadow of the comb (or slits) cast onto the paper. (A point source too would produce ray streaks, though the intensity of light is likely to be reduced.) Note that the height of the lamp filament affects the length of these streaks.

If you make home-made slits which, deliberately, are not perfectly parallel or straight, they can produce wavy rays. The waviness of those rays might help students think about what is said in the previous paragraph: it is all a matter of shadows.

Be ready, therefore, to clarify any misunderstanding that might take place.

Ray diagrams

Misconceptions can also arise from the accepted practice of using only two or three ray streaks in experiments, or rays in corresponding ray diagrams.

The image of an extended object (typically a light source) will be formed from a flux of light passing through the optical system, not just two or three rays. The lens focuses cones of light. Limiting the explanation to two or three rays makes drawing easy, and in many cases correctly predicts the outcome. But without cautions from the teacher, this can mislead and confuse students. For example, many students think that a small opaque disc placed in front of a lens will produce a hole in the image, whereas in practice it simply reduces its brightness. The Newtonian reflecting telescope is a good illustration of an obstruction doing this.

For this reason it is often better to use a multiple slit (or often 5-slit) shutter in front of the ray box rather than the 3-slit shutter normally provided.

This Guidance note was inspired by an article in the journal Physics Education by Prof Laurence Viennot, University Denis Diderot, Paris. [ Physics Education Vol 41 (2006}, 400-408]

Physics Education

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.

In many optics experiments, the apparatus we show is a free-standing lamp on a stand. This may be shielded by housing, which comes in both left and right configurations, to aid in bringing the lamps close. This has several advantages.

• It is easy for students to understand that the object is the glowing filament itself.
• Used with a multi-slit comb, this apparatus produces a broad fan of ray streaks, needed in some experiments.
• Two lamps can be brought side by side to create the top and bottom of an imaginary object. This enables a comparison of the positions of the two lamps in the image produced by a lens. With ray boxes it is difficult to get two lamps close enough together.
• The height of the lamp above the bench is adjustable. When used with slits, this enables the user to alter the length and brightness of the ray streaks it produces.

Ray boxes will produce good rays, but they tend to emphasize parallel incident rays. Some designs have a built-in lens, but this is not always wanted.

A colour filter, such as yellow or magenta, placed in front of the lamp will produce more exciting ray streaks than white rays. A colour filter also helps to identify what happens to light from the top and bottom of an object when the light then passes through a lens. You may be amazed at the difference in response from students.

NOTE: Whether you use a ray box or a simple lamp to produce ray streaks, it is essential that the filament is in the same plane as slits in the comb (i.e. is vertical).

Radiation extends way beyond the visible spectrum, with both longer and shorter wavelengths. The longer the wavelength, the less energy a photon carries. The shorter the wavelength, the more energy it carries.

Infra-red radiation has a greater wavelength than visible light, and is easily measured with a coarse diffraction grating. Beyond the infra-red, radio waves continue the spectrum out through microwaves (short radio waves) to long radio waves with wavelengths measured in hundreds of metres.

Ultra-violet light has shorter wavelengths than visible light, measured by fine gratings operating in a vacuum to eliminate absorption by air. X-rays have far shorter wavelengths, usually less than 10^-10m. A fine enough grating cannot be made, and so instead layers of atoms in a crystal are used.

These radiations are all part of the electromagnetic spectrum. You cannot see such a vast spectrum spread out across a screen. Only a tiny section is visible as light to which your eyes are sensitive. The methods of producing radiation in the various sections are different and so is their detection. Yet all the radiation, throughout the spectrum, travels with the same speed in a vacuum, and the radiation in each section can produce diffraction and interference effects. This shows that it consists of waves. These waves consist of varying electric and magnetic fields.

In diagrams showing the spectrum (see website)...

The Electronic Universe

...the wavelength scale used is one in which equal ratios of wavelengths are plotted rather than equal differences. For example, wavelengths 1 m and 100 m are spaced the same distance apart as wavelengths 10^-2m and 1 m, and 10^-6m and 10^-4m. This is like the scale of octaves used in music, where a jump in the scale of one octave means a doubling of the frequency (and halving of the wavelength}. Such scales are called logarithmic.

Introductory and intermediate level courses

Spectra are beautiful things to see. The full spectrum of white light blazing across a screen is a surprise and a delight to students, even though they have seen a ‘dilute’ version often enough in a rainbow. The full spectrum produced from white light is described as a continuous spectrum, as every colour is present across a range of colours.

Absorption spectra: Absorption spectra are produced when light from a source is partially absorbed by passing through a medium, for example, a beam of white light passing through a green bottle. At intermediate level, colour filters are used to help students to understand the physics of colour. These too are generally continuous spectra.

Line spectra: The ‘single line’ spectrum of a salted flame can come as a surprise: instead of a broad band of yellow, students see a very narrow band of pure yellow, an emission spectrum. Passing white light through sodium vapour produces an absorption spectrum that has a narrow black line at exactly the same place in the yellow. With able students, you might pose the question, ‘how is it that some sources produce a continuous spectrum but others produce a line spectrum?’.

Advanced level courses

In advanced level courses, you can move on and explain why spectral lines are produced.

Energy levels in atoms: Historically, line spectra were among the earliest phenomena to give hints of energy levels and quantum behaviour in atoms, but the hint was not pursued by physicists until other phenomena pointed towards quanta, early in the 20th century. Scientists may now think of line spectra as offering clear evidence for energy levels. In the late 19th century, however, the phenomenon was still a great puzzle.

In advanced level courses, students can follow the argument from frequency differences through the quantum idea to energy levels. Colleagues in chemistry want students to know that atoms have well-defined, discrete energy levels. Amazing stability goes with that: atoms and molecules are completely elastic in collisions, up to a certain limit, above which they can store or release energy in discrete jumps. The experiments and reasoning which led to that knowledge are not directly relevant to its use in chemistry, and so this teaching in chemistry generally rests on simple assertion.

Electron interactions with atoms: Physicists study the stability of energy levels in atoms by experiments in which they bombard atoms of vapour or gas with electrons of known energy. Up to a certain energy, the bombarding electrons bounce off the target atom elastically. They transfer no energy to the atom, beyond the tiny share which is characteristic of the momentum exchange in an elastic collision. Bombarding electrons do not change the energy of the target atom at all. But above a certain minimum threshold value, bombarding electrons make an inelastic collision, giving a sharply defined amount of their energy to the target atom, which is changed to a higher state or energy level. That is shown by the Franck-Hertz experiment (Wikiipedia has information on this experiment} in which, originally, electrons bombarded mercury atoms in warm mercury vapour.

Wikiipedia

In a school laboratory, a similar experiment can be done with electrons bombarding an inert gas such as helium, using a Teltron tube. After inelastic collisions, the atoms of the target gas soon return to their ground state, emitting light as a spectral line. That links up well with a full study of line spectra.

Photon interactions with atoms: When photons bombard atoms, again there are contrasting cases of elastic and inelastic collisions, plain scattering of light and the Compton effect; and the various forms of the Raman effect. These too reveal discrete energy levels in atoms. They also suggest that radiation, from visible light to X-rays, transfers its energy in quanta. A useful animation showing photon emission corresponding to transitions of electrons between atomic energy levels is shown here...

BIGS website

The atomic hydrogen spectrum can be shown with a grating. That spectrum, the Balmer series, has only four lines in the visible region, so students will not realize that the lines are part of a great series. Therefore, to supplement such measurements, you need to show a photograph of the Balmer series extending out into the ultra-violet. Those who like arithmetic puzzles might use the Balmer formula to see if their measurements fit.

Using spectral lines in astronomy: When astronomers look at spectra of distant stars and nebulae, they see spectral lines which obviously come from familiar elements studied in laboratories. These lines reveal the elements present in stars, interstellar space and galaxies.

In the spectra of remote galaxies, however, these lines are shifted towards the red. The red shift is greater for those galaxies which are further away (as judged by other evidence that seems trustworthy). A shift towards the red means a change to a longer wavelength, and also to a lower frequency. This suggests that galaxies are moving apart, and hence that space itself is expanding.

If a bi-convex eyepiece is not used and a plano-convex or meniscus lens is used instead, it should be placed with its plane or concave side towards the eye. That arrangement, which looks like the opposite of the best arrangement for minimizing spherical aberration, is the correct one for an eyepiece. This is because that lens is dealing with small pencils of rays coming from the real image, which the observer is looking at with the eyepiece.

Those narrow pencils are like thick rays, and they are almost parallel to the axis. The eyepiece must deal with these thick rays as well as possible, and for that the eyepiece should have its convex face turned to receive those thick rays. On the other side of the eyepiece the narrow pencils, or thick rays emerging from the plane side of the eyepiece, will pass through the eye ring, so they form a strongly converging group. The eyepiece, arranged this way round, treats those thick rays with less spherical aberration than it would the other way round. Those rays which hit the outer region of the eyepiece lens are bent a little more than the ideal amount, because there is very little spherical aberration. But if the eyepiece were the other way round that extra bending would be much greater, and would have two effects.

• It would give extra magnification to the outer parts of the final virtual image, making distortion.
• It would give curvature of field to the image, so that the outer portions are farther away than the central part.

To see how that curvature of field arises, one must look at the differential ‘extra bending’ between the outer and inner rays of each small pencil. This story of the eyepiece is not something to discuss with students at an introductory level.

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

The aim of producing a model telescope is success, even though students will probably need a lot of help from a teacher who knows just what to tweak to get a good image. Making models of optical instruments gives relevance to studying lenses. The emphasis is on producing a good image of a distant object and using it to look at many distant objects.

Focusing the telescope

The weak, objective lens produces a clear image on a piece of greaseproof paper, which then becomes the object for the eyepiece lens. Teaching a student how to focus the telescope needs a lot of personal encouragement. The teacher is kept busy circulating around the group making encouraging conversation:

"Keep this eye open. Look at the lamp over there with it. Go on looking at it. Think about looking at that lamp. Don’t bother with the other eye, but hold it just in front of the telescope. Go on looking at the lamp with the naked eye, this eye.... Now begin to think about the other eye as well, that is looking through the telescope. It is looking at the magnified image of the lamp. Move the eyepiece until the image looks just as clear as the actual lamp that you see with the naked eye. Go on thinking about the naked eye, but move the eyepiece and you will suddenly see the image just as clear as the lamp itself. Go on thinking about the naked eye. Keep your eyes open in wide-eyed surprise."

Another way to focus the telescope is to use some form of ‘no-parallax’ method.

"Look at the lamp over there with your naked eye. Look through the telescope at the big image. Now move your head sideways, this way and that. If the image is back there on the wall with the lamp the two of them will stay together when you move your head. If the image is much nearer to you, it will slide across when you move your head."

"Hold your hands in front of your face at different distances and stick each thumb up. Wag your head from side to side and watch how the nearer thumb moves to the right as you move your head to the left. If your two thumbs are at the same distance, just side by side, they stay together as you wag your head. Now try that when you are doing a different job with each eye, one eye looking at the lamp, the other looking through the telescope at the image."

Some students will say that because their two eyes are doing separate jobs one eye’s picture floats about on the picture seen by the other eye. This floating is due to a harmless lack of co-ordination. The cure is to say that it doesn’t matter and to suggest rubbing both eyes with the knuckles.

If the observer uses only one eye, and keeps the other eye covered, he can still compare the virtual image and an image-catcher placed above it, by bobbing his head up and down rapidly, then looking alternately at the image and at the image-catcher in rapid succession. This is the only method for those students who have very unequal eyes or one eye that doesn’t see very well.

Teachers might also feel that it takes a lot of time to gain the necessary skill but they will be just as pleased as students when the final image appears clearly back at the object position. Older teachers, using their correct distance spectacles, will be able to see whether the image at infinity is clear because if it is anywhere else then it won’t be clear!

The observer's eye position

It is often difficult for teachers to know what the student is looking at and whether the student’s eye is in the right position. If the lenses are not parallel to each other and perpendicular to the support rod so that the light travels straight through the centres of the two lenses then the final image might not fall onto the student’s pupil. A teacher standing facing a student will be able to see if the light travels onto the student’s eye or lands somewhere else on the student’s head. If the light enters the student’s eye then, hopefully, the student will recognize the image!

Students often say that the image is fuzzy or blurred. With any good lens (or a poor lens used with a small aperture) any object near the axis leads to a good sharp image. Saying that the image is fuzzy or blurred merely means that one is trying to look at it with one’s eye at the wrong distance from it; the image is outside one’s range of comfortable vision. Don't correct that mistaken remark fiercely or insistently at this stage but ask: "Does a book become fuzzy because you move it too close to your eyes? Does your thumb really become blurred because you whip a magnifying glass away?"

Some students may find this unconvincing. Young children have such a wide range of accommodation that they can see an object, or an image, when it is much nearer than would be comfortable for an adult; and their range usually extends ‘beyond infinity’. There is no paradox except in the name. This merely means that the lens system of the eye is so weak that it can bring to focus on the retina a group of incident rays that are already converging. Instead of diverging from an object-point at some distance in front of the person, those rays are converging towards a point some distance behind his/her head. We might call that a ‘virtual object’.

There is an optimum position for the observer’s eye that gives the largest field of view. That is the ‘eye ring’ or the ‘exit pupil’, a small region through which all the emergent light goes. In the model of the telescope, the eye ring is a long way beyond the eyepiece.

The 'eye-ring'

In order to see the eye ring, hold the telescope at arm’s length and point it at a white sky. Look towards the eyepiece. There will be a small, bright disk of light just outside the eyepiece. The disk can be caught on paper so it is the real image of something round.

The eye ring is an image of the face of the objective lens formed by the eyepiece. All the rays of light that go through the telescope come in through a round ‘hole’, the aperture of the objective lens. Any ray of light that hits the eyepiece comes straight to it from some point on the face of the objective lens. When such a ray emerges from the eyepiece, it must go straight through the image of that point on the objective lens. (Any ray from an object-point must go through an image-point; that is the nature of an image!) Thus, all rays which come in through the round hole and hit the eyepiece must then go through the image of that round hole that is formed by the eyepiece. That image, itself a disc, is the eye ring.

The observer wants his eye to receive all the rays which go through the telescope (so that he observes a wide field, fully illuminated), and therefore he should place his eye at the eye ring, because, like any image, that is a place that ‘all rays go through’.

The observer’s own eye-pupil is also a limiting disk. If it is smaller than the eye ring he will use only part of the light that goes through the telescope, the part that goes through a smaller ‘hole’ in the objective than the full aperture. In that case, one might economize and reduce the aperture of the objective.

If the observer’s pupil is larger than the eye ring he will receive all the light that enters the objective and could profit from a still wider objective. However, a wider objective will cost more and its outer regions will produce aberrations, unless the lens is a well-designed compound one increasing the cost still more.

Most instruments are designed to have the eye ring close to the eyepiece, for convenience. The exception is telescope eyepieces on guns.

To locate the eye ring of a model quickly, hold a frosted or opal lamp up against the objective and explore with a scrap of paper beyond the eyepiece.

A model eye and a sectional drawing of the human eye are useful to show students, and links with the biology department can usefully be made when you are teaching how cameras work.

The eye and the camera have a lot, structurally, in common.

• The eye pupil is just a hole which lets the light in.
• The iris is an adjustable diaphragm which controls the amount of light allowed into the eye.
• The retina is a fine network of nerves which are sensitive to light. Most of the adjustment of the eye, between bright sunlight and complete darkness, is done by changes to the sensitivity in the retina so that the range in sensitivity may vary over a million times by storing up light sensitive chemicals for use in low light levels.
• A camera is painted black inside; so is the eye, to lessen trouble due to stray light being reflected.
• Most cameras have a flat film or CCD plate at the back. Some cheap ones hold the film on a curved back to allow for curvature of the image field of their simple lens. The eye has a curved back.

The camera lens must be moved in and out to focus the image of objects at different distances. The eye changes the power of its crystalline lens system by means of ciliary muscles which change the curvature of the lens. The power of an eye differs from one person to another. In round terms, the bending of the cornea is about 40D and the total power may be 60D or more.

The most important thing about the lens is that it can be squeezed to change its power. In an average eye the lens can increase by 4D when it is pulled into greater power to focus something nearby. That change for focusing objects at different distances is called accommodation.

Bear in mind that eyes do not have air in them. The materials inside an eye differ from one another in refractive index. The aqueous humour between the cornea and the lens is salty water that carries chemicals to nourish the cornea. It also presses the cornea outwards to keep it fully rounded. The vitreous humour is a less dense, clear, watery jelly which helps to keep the eyeball fully rounded.

The main refraction of light by the eye is at the front surface, the cornea, hence the success of contact lenses. Since most astigmatism is due to unequal curvature of the cornea, a spherical contact lens can remove astigmatism.

Three parts of the retina are worthy of note;

• There is an interesting patch on the retina where all the nerves of the retina are bundled together into the optic nerve to go to the brain. There are no nerve endings there so it is a blind spot. That gives no trouble in seeing because our eyes scan all the time so you never notice your eye missing anything which falls on the blind spot for an instant. It is easy to show that the blind spot is really there by staring fixedly at X with their right eye, closing the left eye...

• ...while bringing the page nearer. The spot disappears when its image falls on the blind spot. The blind spot is some way from the yellow spot for best seeing(see 3, below.)
• The retina is fed by blood vessels which are just in front of the nerves so that light forming an image goes through them before reaching the nerves. Some people observe a difference in colour due to that red filter when they lie on one side on a sunlit lawn and compare the hues they see with the upper and lower eyes.
• The human eye has a small patch of retina where there are no blood vessels in front. That is the patch used for accurate seeing, as in reading, and is called the fovea or yellow spot. You can learn about the size of it by staring at a book with one eye open and the other closed and estimate the longest word which can be read without moving the book or your eye. However, the eye has a power of 60D or so, the real yellow spot is less than the length of the word. It is at least 20 times smaller and probably less still as it is difficult to keep your eye still when looking at the word. Measurements show it is less than a 1/4 mm wide.

A cheap, fixed-focus camera has such a small aperture that, even if an object is out of focus, the cone of rays from the lens to each image point is so narrow that it makes only a small blur patch if the film catches it too soon or too late. The eye pupil closes down in bright sunlight, thus giving some depth of field. In an emergency, a person who has lost his or her spectacles can read the telephone directory by putting a card with a pinhole in front of the eye and moving closer to the page.