Properties of an Image
The image formed by either a lens or a mirror has certain properties that depend upon the diameter, or aperture, of the objective and its focal length. One property is the size of the image. Si nee the image of a star is a point, size is not an important property for it. For an extended object the image size depends upon the angular size of the light source on the sky and upon the weal length of the objective. Image brightness is important since it determines whether the image is above the threshold of visibility or how long it would take to photograph. The brightness of an image of a point source, such as a star, depends on how much light is intercepted by the objective. Hence its brightness is proportional to the area of the objective or to the square of the aperture. Doubling the aperture but leaving the focal length the same increases the area of the objective or its lightgathering power by four times, concentrating four times as much light into the same-size image.
When we photograph an extended object, the surface brightness of the image depends on the amount of radiant energy per unit area of the image. The objective's area (or the square of its aperture) still determines the total amount of energy collected, but the total energy is distributed over the entire image. Thus the larger the image's area, the smaller the energy per unit of area. The image size of an extended object increases in proportion to the focal length; so for a given telescope aperture the surface brightness of the image decreases as the focal length is made longer.
How well a telescope discriminates between two adjacent objects or shows fine details is called its resolving power. Because of the wave natu re of light, the image of a point source produces a diffraction pattern; it appears as a bright central spot, called a diffraction disk, surrounded by progressively fainter rings. When the diffraction patterns of two stars that are close together no longer overlap, we can see separate stellar images. The larger the telescope's aperture, the smaller is the diffraction disk of each image. A large aperture therefore improves the resolution of closely adjoining features by making the diffraction effect of adjacent objects overlap less. We define resolving power as the smallest angle between two close objects whose images can just be separated by a telescope. This critical angle is directly proportional to the wavelength of the observed radiation and inversely proportional to the aperture of the objective.
