Model of a telescope with ray streaks
Using lamps to model a telescope and measure its magnification.
Apparatus and materials
For each student or group of students
Lamp, stand, housing (one left- and one right-handed), 2
Holder for slit or blocks to hold slit
Plano-cylindrical lens, approximately + 7 D
Plano-cylindrical lens, approximately + 14 D
Pale coloured filter for one lamp (optional)
Power supply for lamps
Health & Safety and Technical notes
Warn students that their lamps may become hot if they are left on for a series of experiments of this type.
The height of the lamp will need to be adjusted to give a balance between brightness and the length of the rays.
The three slits should be placed close to the +7D lens so that the central ray goes, undeviated, through the centre of the lens, and the outer rays go through the edge of the lens. This will reduce the effect of spherical aberration.
The lenses must be carefully placed so that the rays from both lamps only make small angles with the axis of the objective. The eyepiece must be moved so that it treats the two sheaths of rays equally.
a Place the two lamps at one end of the bench to act as the top and bottom of the 'object'. Hold the triple slit about 80 cm or more from the ray boxes. Stand the weak positive lens, +7D, as the objective, just beyond but close to the slits with its curved face towards the 'object'. The eyepiece is the strong positive lens, +14D, which should also have its curved face towards the 'object'.
b With only one lamp switched on, move the eyepiece so that the rays from the lamp emerge to form a parallel beam. Now add the second lamp very close beside the first one. (To make the rays from the second lamp more easily distinguishable, place a sheet of pale coloured gelatine or Cellophane in front of that lamp.)
c The magnification of the object by the telescope can be measured like this: trace the final image rays in a straight line back to the plane of the lamps; then compare the distance between the two lamps with the distance between these two points.
The ratio of the focal lengths:
focal length of eyepiece / focal length of objective
will also give the magnification, and the agreement with the ray result can be checked.
1 With two lamps, students can see that the first (real) image formed by the objective lens is much smaller than the original object (represented by the space between the two lamps). But if students look along the two parallel beams emerging from the eyepiece, they will see that these seem to come from a distant virtual image which is much bigger than the object.
2 A frequent error is to use just one lamp with the three slits, because it is easier, and to assume that the two outside rays come from the top or the bottom of the object. But all the rays come from the same point on the object (the lamp). So a second lamp is needed to represent another position on the object.
3 Colouring the light from each lamp differently makes it easier to discuss what is happening.
Removing the slits so that the full cone of light is seen is a wonderful sight, especially if the beams from the two lamps are differently coloured.
Moving the lamp sideways shows how the images move. The two real images formed by the objective lens will be seen clearly. But the rays, emerging from the eyepiece now form a rather complicated picture, except that the 'eye-ring' will be clearly visible as a place where the two sheaths of rays cross, making a narrow region where an observing eye receives everything. This works especially well if the three slits are being used.
4 Instead of using two lamps, you may use a single lamp and move it to and fro, perpendicular to the axis of the telescope. You will see the emergent beam of parallel rays tilting to and fro much more strongly than the rays arriving at the objective lens. This also illustrates the magnification, but it is not so convincing to beginners as the two-lamp method.
This experiment was safety-checked in January 2007