A telescope is a system of lenses and/or mirrors that makes distant objects appear larger and/or brighter. Today you will experimentally construct a simple astronomical telescope using two lenses. The lenses are converging, that is, parallel rays of light which strike the lens on one side emerge from the other side and converge toward a common point. The light from an extended object like a tree or planet on one side of the lens can form an image of that object on the other side of the lens. The distances from the lens to the object and image are related in the following way:

1/(distance from lens to object) + 1/(distance from lens to image) = 1/(focal length of lens)

where the focal length is a property of the lens as it is made, and depends on the nature and curvature of the glass or plastic from which the lens is made.

An astronomical telescope has at least two lenses (or mirrors). In order to estimate the magnification of the telescope, it is necessary to know the focal lengths of the lenses involved. One can then show that the magnification is approximately

(focal length of lens farthest from eye)/(focal length of lens closest to eye)

The lens farthest from the eye is called the objective lens and the lens closest to the eye is called the eyepiece.

The first project is to measure the focal length of each of your lenses. Note from the first equation above, if the distance from the lens to the object is many times larger than the focal length, then the distance to the image is very close to the focal length. Using this idea, you might be able to form an image of the trees outside on the Quad on a piece of cardboard by carrying your optical bench elsewhere in the building, and measuring the distance from the lens to the image. Since it is difficult to focus the image exactly, you will have a range of values for your focal length. Alternatively, you can use the illuminated object on your optical bench, measure the object and image distances, and calculate the focal length for your lens. However you do it, determine the focal length for each of your lenses. Draw a simple picture of your experimental setup for each determination you make, showing what your measurements mean.

Using the second equation above, estimate the magnification of the telescope you can make with your two lenses. Build the telescope by starting with the lenses separated by a distance which is approximately the sum of the focal lengths, and then adjust the spacing so that you have as sharp an image as you can get when you view the trees outside or other distant objects. The lens with the shorter focal length is the eyepiece.

Estimate the magnification of your telescope by trying to see how many times bigger things are when viewed "through" it than when viewed "past" it. This is easiest to do if you can view an array of equally-spaced objects, like rows of bricks or siding on a house, or marks on a meter stick leaning against a far wall in the room. It helps to make a small "parallel ruler" by cutting a narrow slit in a filing card and holding it near your eye. How does your observation compare with "theory", when you consider the uncertainty in the theory based on the difficulty of measuring the focal lengths accurately?

You might notice that your image is somewhat distorted and has colored fringes on some objects. That is because the lenses are plain and cheap. Careful engineering and use of multiple lenses made of different kinds of glass can improve the quality immensely, as in 35mm cameras and the telescopes we have been using outside.