Using a model telescope
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.
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.