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A classical optical telescope is an example of an afocal system. That is to say, no clearly defined focus is presented either in object or image space. As the name suggests, the telescope views distant objects, nominally at the infinite conjugate and provides a collimated output for ocular viewing in the case of a traditional instrument. As far as the instrument is concerned, both object and image are located at the infinite conjugate. Of course, this narrative does assume that the instrument is designed for ocular viewing as opposed to image formation at a detector or photographic plate. In any case, the design principles are similar. Fundamentally, the telescope provides angular magnification of a distant object, and this angular magnification is a key performance attribute.

The basic layout of a simple telescope is shown in Figure 2.9. Light from the distant object is collected by an objective lens whose focal length is f₁ and then collimated by an eyepiece with a focal length of f₂. These two lenses are separated by the sum of their focal lengths, thus creating an afocal system with an angular magnification given by the ratio of the lens focal lengths.

The matrix of the telescope is similar to that of the compound microscope, with an objective lens and eyepiece separated by some fixed distance.

The separation, s, is simply the sum of the two focal lengths and the system matrix is given by:

(2.13)

The angular magnification (the D value of the matrix) is simply −f₁/f₂. It is important to note the sign of the magnification, so that for two positive lenses, then the magnification is negative. In line with the previous discussion with regard to the optical invariant, the linear magnification (given by matrix element A) is the inverse of the angular magnification. Also, the C element of the matrix, attesting to the focal power of the system, is actually zero and is characteristic of an afocal system.

As in the case of the microscope, the objective lens forms the system entrance pupil. The exit pupil is formed by the eyepiece imaging the objective lens. This is located a short distance, approximately f₁ from the eyepiece, this distance determining the ‘eye relief’. Ideally, for ocular viewing, the pupil of the eye should be co-incident with the exit pupil. Unlike the compound microscope, the exit pupil of a simple (ocular) telescope is relatively large, about the size of the pupil of the eye. Clearly, if the exit pupil were significantly larger than the pupil of the eye, then any light falling outside the ocular pupil would be wasted. In fact, in a typical telescope, where f1 ≫ f2, the size of the exit pupil is approximately given by the diameter of the objective lens multiplied by the ratio of the focal lengths.

As an example, a small astronomical refracting telescope might comprise a 75 mm diameter objective lens with a focal length of 750 mm (f/10) and might use a ×10 eyepiece. Eyepiece magnification is classified in the same way as for microscope eyepieces and so the focal length of this eyepiece would be 25 mm, as derived from Eq. (2.12b). The angular magnification (f₁/f₂) would be ×30 and the size of the pupil about 3 mm, which is smaller than the pupil of the eye.

In the preceding discussion, the basic description of the instrument function assumes ocular viewing, i.e. viewing through an eyepiece. However, increasingly, across a range of optical instruments, the eye is being replaced by a detector chip. This is true of microscope, telescope, and camera instruments.