Optical instruments

Lens

Light, Sound and Waves

The magnifying glass: qualitative

Practical Activity for 14-16

Class practical

Simple demonstration of how the magnifying glass works.

Apparatus and Materials

For each student
Spherical lens +7D

Health & Safety and Technical Notes

Read our standard health & safety guidance

If students wear spectacles for reading it is best to keep them on for this experiment.

Procedure

Students can be given these instructions:
"Hold the lens very close to your eye with one hand. Hold the thumb of your other hand at the right place for looking at it with this magnifying glass. Move the thumb nearer and then farther away until you see it clearly in focus. Then remove the lens and see whether you can still see your thumb."
Next you should say:
"Now put the magnifying glass back. You can see your thumb comfortably and it looks large. You are looking at an image of your thumb. Where must that image be?"

Teaching Notes

The positive lens acts as a magnifying glass.
This is a simple observation of the image of an object placed between the lens and its focal plane. The image must be on the same side of the lens as the object. With normal vision it must be between 25 cm and infinity in front of you, and so is further away than the object. This is a virtual image. The light only appears to have come from the image to your eye. You cannot catch a virtual image on a piece of paper.
When the lens is removed, your thumb is still there, but it looks fuzzy. It is too close for you to see it in focus, because the eye is unable to form an image of it on the retina. It is much closer than your eye's near-point of comfortable seeing. You cannot change the lens inside your eye enough to focus it.
The magnifying lens allows you to bring the object nearer to your eye, and so the image appears to be bigger than the object. If the image is three times as far away as the object is from the lens, then the image will be three times as tall.

This experiment was safety-tested in January 2007

Light, Sound and Waves

The magnifying glass: quantitative

Practical Activity for 14-16

Class practical

Finding the position and size of the image in a magnifying glass, and hence the magnification.

Apparatus and Materials

For each student or group of students
Telescope mount or metre rule with Plasticine or Blu-Tack
Plano-convex lens, + 14D
Graph paper (2 mm), sheet
Wooden strip or tongue depressor
Retort stand and bosses (2 if metre rule is used)
Bright lamp to illuminate the object

Health & Safety and Technical Notes

Read our standard health & safety guidance

This experiment is more easily performed using a commercial mount. If a metre rule is used it should be firmly fixed horizontally using the retort stands and bosses.

The object '0' and the image-catcher I are made by attaching pieces of graph paper to the wooden strips. These in turn are fixed in the holders in a vertical position. The top of I should be higher than the lens. The top of '0' should be level with or just below the top of the lens. The object must be very well illuminated by a lamp close to it.

Procedure

Fix the +14D lens in a holder on the mount, to act as the single magnifying glass, with its less convex side towards the observer.
Position the image catcher I 25 cm from the lens (the average near-point of comfortable vision). Place the eye close to the lens L and move the object '0' until its image seems to sit clearly on the catcher. To make this adjustment, keep both eyes open, looking at the catcher with one (naked) eye, and looking through the lens at the virtual image of the object with the other eye. Concentrate attention on the naked eye, continuing to keep the catcher in focus. Meanwhile move the object nearer and farther away, until the eye looking at the image sees that image also sharply in focus, sitting on the catcher.
The magnification may be estimated. Or you can simply observe that the image is back at the image-catcher, and obviously considerably bigger than the object.

Teaching Notes

An alternative method, which is neither so easy nor such good teaching of the meaning of images, is the 'method of no-parallax'. Keep both eyes open and (concentrating attention on the naked eye) move the head to and fro laterally, moving the object until image and catcher seem to stay together.
There is a third, poorer method, only to be recommended where a student has uneven eyes or can use only one eye well. The head is moved up and down rapidly, looking through the lens at the virtual image, then over the lens at the catcher, then through the lens at the image, and so on. During this rapid alternation of glimpses of image and catcher, the object is also moved until both image and catcher seem, successively, equally in focus.
The sizes of the object and the image on the graph paper may be compared and hence the magnification calculated.

This experiment was safety-tested in January 2007

Lens

Light, Sound and Waves

Compound microscope

Practical Activity for 14-16

Class practical

Making a model microscope and measuring its magnification.

Apparatus and Materials

For each student or group of students
Telescope mount or metre rule with Plasticine or Blu-Tack
Plano-convex lens, + 7D (14D if possible)
Plano-convex lens, + 13D (20D if possible)
Graph paper (2 mm), sheet
Wooden strip or tongue depressor
Retort stands and bosses, 2
Greaseproof paper
Microscopes, selection of

Health & Safety and Technical Notes

Read our standard health & safety guidance

Graph paper fixed to a holder or wooden strip makes a good object provided it is very well illuminated. A translucent scale illuminated from behind is better. (This could be a transparent ruler or greaseproof paper with a scale marked on it.)

Procedure

Set the support bar or rule at head height for comfort in manipulating the lens positions.
Place the object near the far end of the support rod. Fix the + 13D objective lens about 10 cm from the object.
Pick up a real image of the object on a piece of greaseproof paper, placed about 30 cm from the objective on the observer's side, by moving the object.
Place the + 7D eyepiece lens near to the image on the greaseproof paper, so that it acts as a magnifying glass for this image. When the greaseproof paper, is removed the final virtual image can be clearly focused by moving the eyepiece slightly backwards and forwards.
Move the lamp around to the front of the object so that it illuminates the object from the front. With both eyes wide open, look directly at the object with one eye, whilst the other eye looks through the microscope. Concentrate on the naked eye, and move the eyepiece so that the image is still clearly in focus with the image sitting on top of the object. The magnification can be measured by comparing the graph paper scales of the object and the image.
The student usually tries to place their eye close to the eyepiece but, in fact, as they move their head faster back from the eyepiece, their field of view increases until it reaches a maximum. Students should find the eye position for the largest field of view. This is in fact the exit pupil or eye ring and may be about 10 cm from the eyepiece.

Teaching Notes

In a microscope, the objective lens makes a large, real image of a near object, whereas a telescope objective makes a small real image of a distant object. An eyepiece is then used as a magnifying glass to magnify this real image.
With the distance between the lenses about 50 cm, a magnification of about 6 is obtained. A useful applet for calculating the likely magnification is provided on the Hyperphysics site.
After students have made this model microscope, have them use a selection of professional microscopes. They should be able to adjust them so that the image is at their near point, near to the object, so that there is no eye strain. Knowledge of microscope design might help at this point.

This experiment was safety-tested in January 2007

Lens

Light, Sound and Waves

Making a telescope

Practical Activity for 14-16

Class practical

Using two convex lenses to make a simple astronomical telescope.

Apparatus and Materials

For each student or group of students

Telescope mount or metre rule with Plasticine or Blu-Tack
Retort stand and bosses, tall
Convex lens (+14 D), plano-convex if available
Convex lens (+ 2.5 D), plano convex if available
Greaseproof paper or frosted screen
200-watt carbon filament lamp (one per class)
Mounted lamp holder (one per class)

Health & Safety and Technical Notes

The mains lampholder must be fitted with a suitably-fused 13 A plug. It is best if the batten holder is one of the safety pattern where inserting the bulb operates a switch.

Read our standard health & safety guidance

Suitable plano-convex lenses are available from the supplier: ASCOL.

It helps if the room is three-quarters blacked out.

Procedure

Put the weak + 2.5 D lens in a holder at the far end of the mount or fix it firmly to the metre rule with Plasticine or Blu-Tack. If it is plano-convex, the convex face should be towards the object.

Raise the telescope mount to shoulder height. Turn and tilt the mount until it is aimed at the distant lamp. Catch the real image of the filament on a scrap of tissue or greaseproof paper - like the back of the pinhole camera.
Install the eyepiece, + 14D, as a magnifying glass to view the scrap of tissue with one eye. Again, if a plano-convex lens is used, the convex face should be towards the tissue. (The system is not symmetrical.)
Slide the magnifying glass nearer and then farther until you see the scrap clearly magnified and in focus. A partner could hold the greaseproof paper to enable the observer to slide the eyepiece. Encouragement to watch the place where the paper is also helps.
Take away the tissue, so that you are looking through a telescope at the lamp, with one eye.

Open the other eye and use your two eyes to get the telescope properly focused. For comfortable use, the final image should be as far out as the object.
The eye at the eyepiece looks through the telescope at an image of the distant lamp; while the other eye, the naked eye, looks straight at the distant lamp.
Does the telescope picture of the lamp look larger than the picture seen by the naked eye?
If they are not both in focus at the same time, move the eyepiece forwards or backwards a little until you do see both clearly at the same time. You could say to students:
Raise your eyebrows and keep your eyes open with "wide eyed surprise".
Direct the telescope at familiar objects and look out through an open window. DO NOT LOOK AT THE SUN - take care that this is not possible. This could damage students' eyes badly.

Teaching Notes

Looking at the printing on spines of books across the room can persuade students that their telescopes do really magnify. They may be surprised to find that the telescope image is inverted; this can make it hard to scan a scene.
A look at the Moon is not only a special delight; it can persuade pupils who have found focusing their telescope difficult, to succeed at last. (A half moon shows the mountains particularly near the edge: a full moon glares.)

This experiment was safety-tested in February 2007

Lens

Light, Sound and Waves

Telescope magnification

Practical Activity for 14-16

Class practical

Measuring magnification by direct comparison of object and image.

Apparatus and Materials

For each student or group of students

The telescope as constructed in the experiment Making a telescope
Carbon-filament lamp for preliminary focusing
Paper scales, tall
Reading lamp, with shades, to illuminate scale

Health & Safety and Technical Notes

The mains lampholder must be fitted with a suitably-fused 13 A plug. It is best if the batten holder is one of the safety pattern where inserting a bulb operates a switch.

Read our standard health & safety guidance

Each scale should be vertical, with horizontal lines on it to act as an object when the magnification is estimated. A strip of shelf-paper can be used, or one or two sheets of A3 paper taped end to end. Rule thick horizontal lines on it every 10 cm, to make a coarse scale. The lines should be numbered. The experiment is easier if successive lines are drawn in different colours.

It helps if the room is three-quarters blacked out. Since the scale is vertical, it may be viewed obliquely, so telescopes may be spread out at the other end of the room.

Procedure

Post the scales, high up, at each end of the room. Illuminate them with shaded lamps to prevent glaring the observers' eyes.

Direct the telescope at the scale, and focus it so that the final virtual image of the scale rests on the scale itself. Then, keeping both eyes open, estimate the magnification by concentrating the telescope eye on one division of the image, and seeing how many divisions of the original scale the image division covers.

Teaching Notes

You might suggest that students measure the focal lengths f₁ and f₂ of objective and eyepiece - just roughly by catching a window's image on an opposite wall - and see whether f₁ / f₂ agrees with their estimate of magnification.
The magnification will be found to be the ratio of: the focal length objective lens divided by the focal length of the eyepiece lens.
The separation of the lenses will be the sum of the focal lengths f₁ + f₂. At that spacing of the lenses, the telescope is referred to as being in normal adjustment.

This experiment was safety-tested in February 2007

Lens

Light, Sound and Waves

Using the telescope like an astronomer

Practical Activity for 14-16

Class practical

Placing the final image at reading distance from the eye, as an astronomer would.

Apparatus and Materials

For each student or group of students

Telescope mount or metre rule with Plasticine or Blu-Tack
Retort stand and bosses, tall
Convex lens (+14 D), plano-convex if available
Convex lens (+ 2.5 D), plano convex if available
Greaseproof paper or frosted screen
Mounted lamp holder (one per class)
200-watt carbon filament lamp (one per class)

Health & Safety and Technical Notes

The mains lampholder must be fitted with a suitably-fused 13 A plug. It is best if the batten holder is one of the safety pattern types, where inserting a bulb operates a switch.

Read our standard health & safety guidance

Procedure

Hold a page of print beside the telescope, about 25 cm from your eye. Look at the remote lamp through the telescope with one eye, while you read the print with your other eye.
Concentrate hard on the naked eye, while you move the telescope eyepiece to bring the lamp into focus.

Teaching Notes

This is the same procedure as in the experiment Making a telescope, but try to place the final virtual image only 25 cm away - as an astronomer who wished to make sketches in a notebook would place it. The astronomer would want to move quickly from telescope to notebook without having to re-focus their eyes.
If a student finds this too difficult, yet wants to succeed, do the focusing for them. Let them have a good look, with both eyes open; then move the eyepiece and let them try for themselves. This works well for a student who is held back by not knowing what to look for.

This experiment was safety-tested in March 2007

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.

Ray Diagrams

Light, Sound and Waves

About telescope lenses

Teaching Guidance for 14-16

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.

Lens

Light, Sound and Waves

Using a model telescope

Practical Activity for 14-16

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.

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