Telescope is a basic tool of the astronomer to broaden our knowledge of the universe.

Basic Elements of Telescope

Telescope, a two-lenses system, can be either refracting ( the objective is a lens) or reflecting ( the objective is a mirror). It is formed by eyepieces lens and objective lens and the lenses are separated by a distance equal to the sum of their focal lengths.

  • An eyepieceis a device which acts on an object and presents its image to the eye a much larger angle.
  • An objective is the lens closest to the object that forms the initial image in an optical system. In a telescope, the image formed by the objective lens is an intermediate image.

    Astronomical telescope in which the image is inverted, is one of the two principal types of the telescopes. Its primary function is to enlarge the retinal image of a distant object. In the illustration (Fig. 1)below, the object is at a infinite distance form the objective, so that the intermediate image is formed in its secondary focal plane, which also coincides with the primary focal plane of the eyepiece. Then the eyepiece forms a virtual inverted image of this intermediate object at infinity. Both object and resulting inverted image are at infinity in this configuration. Also because of this configuration, the field stop of the telescope must be place at the intermediate image. To focus on an object, the eyepiece adjusts, while the intermediate image is fixed. The inverted image is not a problem, as long as the scope is used for astronomical observations since most work is photographic. Fragments of space that are captivated by the telescopes, are not rendered inverted, given that space has no “upside or down”. This is showed below.

    (FIGURE 1) Rays paths in a astronomical telescope system: the length of the telescope, L, becomes sum of the focal lengths, L= f1 + f2. 

    Mathematical Properties of Telescope

    This can be done through the ray tracing using the transfer matrix so the system matrix becomes:

    The ray-transfer from a plane at a distance d in front of the objective lens, to a plane at a distance d behind the eyepiece lens, is now given by the transfer matrix:

    Then the matrix reduces to

    where =y’ y is the magnification (where y’ is the image height and y is the object height). But, in contrast to other imaging systems, we now have the same magnification:

    In order to collect as much light as possible from a distant object, the objective should be as large as possible. However, in order to have large lenses manufactured, there are obvious problems. For example, it is essential to have the same optical properties throughout the lenses. Otherwise, any internal bubbles will alter the refractive index in those regions. Furthermore, lenses such as achromatic lenses tend to suffer from a residual amount of chromatic aberration (ie. optically dispersive). To overcome these difficulties is to build a telescope using parabolic mirror by the Newtonian design. However, most of the world largest telescopes nowadays employ the Cassegrain design. The advantage of this design is the beam-spreading qualities of the secondary mirror, which means that the effective focal length is several times that of the primary mirror. This allows for relatively more compact, easily-engineered, cost efficient and larger telescopes compared to telescopes engineered with Newtonian Design.

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