Light Gathering Power of a Telescope

It is necessary that a telescope have a high magnification to get a good image of astronomical objects. Having a high magnification is only part of getting a good image, not least since distortions of the atmosphere limit the size of objects that can be resolved to 1 arc second or greater. In fact, for a telescope in normal adjustment, the magnification is equal to the ratio of the focal lengths of the primary or objective, and the secondary, or eyepiece lens, so it is possible to claim a high magnification just by having an eyepiece lens of very short focal length. Some cheap telescopes claim to have magnifications of several hundred, by this method, but this is misleading. As important, and often more important than magnification, is light gathering power. Light gathering power is proportional to the area of the telescope. If the diameter of a telescope lens double, the light gathering power increases by a factor of 4. If the diameter of a telescope increases by a factor of 3, the light gathering power increase by a factor of 9, and so on..
Having a high magnification telescope with a small aperture, or primary lens, will only increase the size of the blurry image. To get a good image, you must increase the size if the aperture. This will increase the light gathering power, and allow smaller detail to be resolved according to Rayleigh's Criterion:  
\[\theta \simeq \frac{1.22 \lambda}{D}\]
, where
  is the angular size of the detail
  is the wavelength of light being used to observe the object
  is the diameter of the lens or mirror.

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