The telescope and the collected energy: Illumination
 

If a screen is placed in the focal plane of a telescope, an extended source provides it with an illumination, , this being defined as the amount of collected flux that is concentrated into unit area of the screen. It is obvious that when the image is recorded on a two-dimensional detector (photographic plate or electronic detector), the length of exposure required depends on the strength of the illumination. Using the identities defined in the previous subsection, the flux collected by a telescope from an extended source is
BωA_T

and the area of the image is given by
F²ω.
Hence, the illumination is given by

If D is the diameter of the telescope collector, then the illumination of the image is, therefore, given by

and, therefore,
(1)
where f is the focal ratio of the telescope. As mentioned briefly earlier, the correct exposure times for landscape photography can be adjusted by altering the focal ratio of the camera lens. When recording the image of an extended astronomical source with a fixed focal ratio telescope, the required exposure time is governed by the brightness of the source and the focal ratio, not the physical size of the telescope collection area.
One implication of this result is that for a range of telescopes of different sizes but with an identical focal ratio, although the flux collected increases with telescope size, so does the image size and the illumination to the image of a particular object is constant. The collected flux increases as the square of the telescope’s size and the area of any image also increases in the same proportion. However, as the size of image increases by using a larger telescope, more detailed spatial studies may be made. Thus, we may summarize one of the uses of the telescope as being its ability to achieve angular resolution, allowing spatial analysis to be made of the radiation arriving from an extended source.