Topic 40. The astronomical telescope

The astronomical telescope is similar in design to the compound microscope discussed in the previous topic. However, unlike the microscope, which is designed to view objects that are small and nearby, the telescope is designed to view objects that may be large, but are very far away.

As with the previous instruments, the magnification of the astronomical telescope is with respect to the performance of the unaided eye. If the distance between the eye lens and the retina is d, and if the object to be viewed is at a much greater distance D away, then the magnification of the eye lens itself is simply d/D, which is a very small number. The magnification of the telescope will be relative to this value.

The astronomical telescope consists of two lenses as shown in the following figure. The first lens, called the objective, has a focal length that is as long as possible. The focal distance of this lens is shown as “f” in the figure.

Since the object is a very great distance away, the first lens forms a real, inverted image just beyond its focal point.  (The distance beyond the focal point of the objective lens is exaggerated in the figure above.)  The magnification of the first lens is approximately f/D. Since D is a very large distance, this magnification is generally a very small number too.  Nevertheless , although f/D may be a small number, it is already larger than the magnification of the eye lens by itself, which is only d/D, where d is the distance between the eye lens and the retina. The reason for this improvement is that the objective lens can have a focal length that is much greater than the focal length of the eye lens, which is roughly the diameter of the eye itself.

The real image formed by the objective lens acts as the object for the second lens, which is the usual simple magnifier. The second lens is positioned so that the image formed by the first objective lens is essentially at the focal distance of the second lens, which is shown as “F” in the figure. (The distances are exaggerated in the figure above.) Since the eye is positioned just behind the eye-lens of the telescope, the combination of the eye lens in the telescope and the lenses in the eye take an object that is essentially a distance F in front of the lens combination and produce an image on the retina a distance d behind the combination. The magnification of this combination is therefore d/F. The eye-lens in the telescope often has a small adjustment range to compensate for the different strengths of the eye lens and cornea in different people.

The magnification of the combination is the product of the two, or

The magnification is thus the product of two terms which can be re-arranged as shown. The first is the ratio of  the focal lengths of the two lenses in the telescope and the second is the magnification of the eye lens acting by itself. The telescope therefore improves on the eye itself by the factor f/F. To maximize this value, the focal length of the first lens must be as long as possible and the focal length of the second lens must be as short as possible. The second criterion is the usual result for a simple magnifier.

From the figure, the separation between the lenses is the sum of the two focal lengths, so that increasing the focal length of the first lens increases the length of the instrument by the same factor. Thus a high-magnification version of this design tends to be a very long device – while decreasing the second focal distance can compensate to some extent, the second focal distance is usually so short already that its value does not make a significant contribution to the total length of the device. The length is sometimes made somewhat smaller by folding the length using prisms or mirrors. This is usually done in binoculars.

There is the usual trade-off between magnification, which increases as the focal length of the first lens is made longer and light-gathering power, which depends on the inverse of the f/number of the first lens and therefore decreases as the focal length is made longer so that the f/number is made greater. As with the microscope, many designs increase the diameter of the lens to keep the f/number at a reasonable value, but here the tendency is in the opposite direction from the microscope – that is, towards increasing the focal the length of the first lens  (to increase the magnification) and simultaneously  increasing  its diameter (to keep the f/number and therefore the light-gathering ability at a reasonable value). The design criteria in the microscope tended to push both values in the opposite direction – towards smaller focal lengths and smaller diameters.

Note that the image produced by this telescope is inverted. This is usually not serious for astronomical observations, but a telescope designed for terrestrial use (binoculars, for example) usually have a second positive lens in the optical path that inverts the image again so that the observer sees an erect image of the distant object. This inversion can also be done with other optical elements (prisms, for example).