Experiments with a fan of rays
A group of short, introductory experiments to investigate the behaviour of concave and convex lenses using rays of light.
Apparatus and materials
Metal plate with five parallel slits or multiple slits (e.g. a wood-graining comb)
Holders for slits and barriers
Cylindrical lenses (see technical notes)
Power supply, 12 V
Ray box, with vertical filament
Lamps with vertical filaments
Health & Safety and Technical notes
Many ray boxes of traditional design become very hot after a lesson of use. The class should be warned, and provided with heat-resistant gloves or cloths if they need to handle the ray box when still hot.
1 Ideally you will provide plano-cylindrical lenses, with powers of about + 7 D (f=14.3 cm), + 10 D (f=10 cm), + 17 D (f=6 cm) and - 17 D (f=-6 cm). The most commonly available at the time of writing (Jan 2007) are + 7 D, + 13 D, - 7 D and - 13 D, generally biconvex and biconcave. These will perform the experiments as written, although plano-convex or plano-concave lenses will enable the aberrations to be reduced. The lenses should be 5 cm wide in order to give extensive fans of rays, and 5 cm high so that the rays extend a great enough distance.
Plastic lenses have steeper curves for the same powers compared with glass lenses and the aberrations are therefore much greater (glass has a higher refractive index than plastic).
2 Do not give students all the lenses, slits, etc., straight away. At the beginning they should have the lamp and power supply, a multiple slit, barriers, white paper, and just one lens, the weakest convex lens (probably + 7 D). Later give samples of all the lenses for a short period of general play, with a warning that lenses are rather fragile and are easily scratched. After that, it is best to provide only those lenses, etc., that are needed for each experiment.
3 A screen with 5 or more slits is preferable to the 3-slit screen supplied with most ray boxes. If it is possible to provide home made screens like this, the effect will be increased. Such a screen can be supported in the path of the beam coming from the box. In these experiments a 'multiple slit' refers ideally to one of these. The spherical aberration of experiment e will not show with a 3-slit screen.
4 If the ray looks fuzzy, it may be because the lamp filament is not vertical, parallel to the slits in the screen. Or it may be because the lamp has a crooked filament. In the latter case, the cure is to change lamps. The crooked filament can, in some cases, even give an impression of crooked rays. Home-made slits which are not really straight and vertical are also apt to produce crooked rays.
5 The shields for the lamps come in two slightly different designs; some are placed around the lamp but others are big enough to put the supporting arm of the lamp into the half-length slot, allowing the light to come out of the long slot. It is worth experimenting to see which is the best way for your equipment.
6 For all the experiments, three-quarters blackout is strongly advised.
a Fan of rays of light
Shine light from the lamp through the multiple slit and make 'rays' on the paper, which is laid on the bench in front of the lamp.
Raise or lower the lamp until the rays continue right across the paper.
b Rays and lenses (first + 7 D; later various lenses)
Place the weak positive cylindrical lens (+ 7 D), in various positions in the fan of rays produced ina, and look at what it does.
For a short time, try out other lenses available in place of the + 7 D lens.
Return to the + 7 D lens and try using barriers to cut down the aperture of the lens.
c Lens forming a real image
Carefully adjust the + 7 D lens to ensure that its face is perpendicular to the central ray. Shut down the aperture if necessary until all the rays that come through seem to go on through one point. This is a 'real image'. Again, try other lenses in this way.
d Fan of rays and two lenses
Use two lenses of the same power (e.g. + 7D, in the fan of rays. Try the lenses different ways round and observe any effect.
e Fan of rays and a stronger lens
Replace the lenses with the single strongest convex lens available (probably + 13 D or + 17 D). Use barriers to restrict the aperture and lessen the spherical aberration.
f Fan of rays and a negative lens
Replace the positive (convex) lens with a cylindrical negative lens (concave, probably - 13 D or - 17 D). Look along the rays from the outgoing end and see 'where they seem to come from'. Also look from above and again 'see where the rays seem to come from'.
Move the lamp towards and away from the lens and note the changing position of the virtual image.
Effect on image of changing object distance
g Changing object distance
(using lens + 7 D, later with + 13 D or - 17 D)
Go back to the weak positive lens and try moving the lamp nearer and farther away. You can also try this with the strong positive lens.
Observe that a clear image is always formed and that the distance of the image from the lens depends on how far away the lamp is from the lens.
h Virtual images
Once more with the weak positive lens, move the lamp so close to the lens that a virtual image is formed. Look along the rays from the outgoing end and see where the rays seem to come from. Then look at the rays from above and see where they seem to come from.
1 Students should begin to realize that the light travels in straight lines and that an object is seen when light enters the eye. A lens bends light rays so that the rays pass through an image point. We think we 'see' the object at the image point.
2 It is worth spending time organizing the students at the beginning so that they can get the equipment set up quickly and safely. Power supplies, in the darkened laboratory, can have dangerously trailing cables. Lenses have a nasty habit of 'getting themselves' underneath heavy power supplies too. If the initial organization is done well then this will help the students to work at their own pace. Diagrams can be drawn by putting paper on the ray streaks and sketching over them.
Carry out the experiments as a continuous programme, with students moving at their own speed. In this way, extension work for faster students can be encouraged. The division into separate parts a, b, c . . . in these notes is an artificial one, intended only to help when you are making preparations.
3 The rays of light passing through the comb are just like a sunbeam travelling through patchy clouds. The length of them can be adjusted by raising and lowering the lamp.
4 With step b, visit the students to make sure that they have tried placing the lens so that it is not twisted, but receives the rays more or less 'normally'. Offer them small barriers to shut off some edge rays if they wish.
This is a new amusing game for young people and they will do many things with the lenses which do not seem sensible or profitable to a physicist. They do not know what properties of lenses and rays they are looking for, and we suggest that you should respect that ignorance and let them play quite freely for a while. Suggested lenses are + 17 D; - 17 D; an extra + 7 D, and perhaps a plane mirror.
The rays from a single point object (the filament) do, after passing through the lens, pass through an image point and go straight on through it. The lens can be twisted with respect to the rays, and turned so the plane or convex side is facing the incident beam of light.
5 Again, in step c, encourage students to ask for more lenses. This may seem like a repeat experiment. But it is a time for students to show that they can produce a good image by placing the plane side of the lens towards the lamp (if they have plano-convex lenses) and the lens perpendicular to the central ray. (The rays will otherwise fall on a caustic curve after they pass through the lens.) This is exciting in its own right, and shows the effects of astigmatism. Closing down the aperture will show the effect of only using the paraxial rays on the sharpness of the image. The lamp can be moved sideways, and backwards and forwards, to show the effect on the image position.
6 Whichever way round the stronger lens is placed in step e with respect to the incoming rays, the lens seems to suffer from a 'problem'; all the rays do not go through a single image point, and some of the rays may be coloured at the edges. To get a good image the lens should be 'stopped down' (aperture reduced) and turned (if it is plano-convex), so that equal amounts of refraction take place at each surface; the screen receiving the image can then be placed at the 'circle of least confusion'. In optical instruments the problem is solved by adding together a number of lenses to produce the same refraction and the 'misbehaviour' of one lens is compensated for by the opposite behaviour of another.
Spherical aberration is natural, optical behaviour. It results from rays of light being bent, according to the law of refraction, at the surfaces of a spherical lens. Fortunately, a spherical lens does produce an almost perfect image for rays from a point object, when the object is near the axis of the lens and the aperture is small, so that none of the rays hit the lens surfaces very obliquely.
7 Step f will raise questions of virtual images, but there is no need to labour the idea at this stage (see teaching note 8). We can show rays which spread out after passing through a concave lens as though they have come from a point near to the lamp. The rays don't actually pass through a virtual image. By looking along the rays, from the opposite end to the lamp, the rays will appear to be straight.
It is also interesting to show what happens when the - 13 D or - 17 D lens is teamed up with a + 13 D or - 17 D lens; the joint effect of the lenses is to behave like a parallel block of glass.
8 Students should not make any record of the changes of image distance in step g. The purpose of this experiment is to let students see that a clear image is always formed and that the distance of the image from the lens depends on how far away the lamp is (using the word 'image' in the sense of a place through which rays cross accurately). As the lamp distance becomes less, the image distance becomes greater. If the distance between the lamp and lens is less than one focal length, the lens will produce a virtual image. The 'special position' of the lamp at the focus of the lens producing parallel rays after passing through the lens could be noted.
Moving the lamp sideways (if practicable), perpendicular to the rays, will produce an image which is off the principal axis of the lens.
9 Step h is the time to discuss virtual images with students while they are looking at their lens and rays together. (This is not a good time for a demonstration. This would interrupt and spoil this period of students' own explorations.) A + 7 D lens placed near to the lamp shows the rays spreading out after passing through a convex lens, producing a virtual image. Looking along the emergent rays towards and through the lens, the rays appear straight, not even bent by the lens. Looking above the rays, the emergent rays will appear to meet on the same side of the lens as the lamp.
10 When students are doing experiments with lenses receiving a fan of rays, it may help if you move round amongst them, to straighten a lens or offer an extra lens to try. You can slide a small piece of cardboard in across the fan, to cut off ray after ray. The demonstration of successive rays being cut off or admitted seems to help students to understand what is going on. You can do this at any point in this sequence of experiments.
This experiment was safety-checked in January 2007