One of the simplest image-forming devices is a concave mirror. If the mirror is parabolic, on-axis rays which makeup a parallel beam are deflected and converge at a single point. The radiation from different parts of an extended object, such as a galaxy, reach the mirror from slightly different directions . They are then deflected and brought to a focus at slightly different points in the FOCAL PLANK of the telescope to form other elements of the image.

The formation of an image is more complicated than thin in practice. Electromagnetic waves consist of rapidly-varying Electric and magnetic fields. If these waves are to add together to produce a sharp , luminous image it is important that they all reach the focal plane of the telescope with approximately the same PHASE .Otherwise the radiation in the out-of-phase waves will subtract from the total, reducing the net luminosity of the image. This gives the most important constraint on the precise shape of the mirror of the telescope, namely that all the rays in A parallel beam incident on the telescope should reach the focal plane With approximately the same phase In practical terms, it is usual to require the shape of a telescope to be accurate to within about one-twentieth of the wavelength of the radiation the telescope is designed to collect. This means that an optical telescope working at a wavelength of 500nm has to be polished to within =25nm, whereas a radio telescope working at a wavelength of 21cm may be built much more crudely with a surface accuracy of only 1 cm.

Another important parameter of a telescope is the area of the radiation collector. The larger the telescope, the more radiation can be gathered {in proportion to the square of the diameter of the telescope). A larger telescope means that observations may be made more rapidly and of much fainter objects .It also improves the amount of detail visible in the image. This is set by the resolution of the telescope in the following way. Suppose that there are two objects, such as stars, close together on the sky. If we are to resolve them, that is to form images of the two objects which do not overlap, then we require that the radiation forming the image of one of the objects must not add together to give an appreciable signal at the position of the image of the other object. The first object is on the axis of a telescope of diameter D which works at wavelength A. The rays from the second object travel in a direction which makes a very small angle with the rays from the first object (this angle is the ANGULAR SEPARATION of the two objects in the sky). Some of the radiation from the second object is reflected to the position of the image of the first object, that the rays from the second object to the edges of the telescope have a path-length difference of L between them. This path-length difference produces a phase difference in the received rays which reduces their net intensity. When I – ? /2 the extreme rays are of opposite phase and we see that ? = ? /2D (since ? is small so sin ? = ?). It is usual to define the RESOLVING POWER of a telescope as the smallest angle between two point objects that produces distinct recognizable images. It is usually given as ? – 210000 ? /D arc sec.

The larger the telescope, or the shorter the wavelengths used, then the better the resolving power. However it is not always possible to improve the resolution of a telescope indefinitely. An optical telescope of 10cm diameter has a resolution of about 1 arc sec. If the diameter was increased to 1 m, the telescope itself would have a theoretical resolving power of 0.1 arc sec, but we have seen that the radiation which has passed through the Earth’s atmosphere is spread over an angle seldom less than 0.5 arc sec by fluctuations in the atmosphere. For this reason the largest optical telescopes in the world have resolving powers no better than that of 20-cm telescopes – but they are able to gather much more radiation than small ones. Because of the longer wavelengths they use, infrared astronomers are much more affected by diffraction limits than optical astronomers. At a wavelength of 10 ?m, a 2-m telescope has a diffraction-limited resolving power of about 1 arc sec – again the limit of seeing at these wavelengths.

We will find it convenient to talk about the FOCAL RATIO (or F-RATIO) of a particular telescope focus. This is the ratio of the effective focal length of the telescope to the diameter of its primary reflector. The focal length of a telescope is the distance of the focal plane from the mirror. The MAGNIFICATION of the image is proportional to the focal length of the telescope. Note, however, that large magnifications can be undesirable for faint objects if their light is spread over too great an area.

Radio waves are much less affected by the Earth’s atmosphere and the size limits of radio telescopes are set largely by difficulties of construction. These problems may be avoided by the use of interferometers (described later). At a wavelength of 2cm, an interferometer of 5-km baseline has a resolving power of about 1 arc sec.

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