It has often been claimed that photography is painting with light, and it is this light I will now consider.
Film and digital sensors do not record the range of luminosity that a healthy eye can see. When photographing a scene we have to compromise between seeing the details in the shadows or in the highlights. OK so now you can combine two or more images using computer software to expand the dynamic range (HDR).
However ignoring HDR the photographer has to decide between exposing for shadows, mid-range or highlights and accepting the loss of detail.
Let's assume we are are going for mid-range exposure. The correct exposure is the same as saying the correct amount of light. This is determined by three factors
ApertureThe amount of light passed through the lens is directly proportional to the area of the lens. As this is circular this makes the amount proportional to the square of the diameter.
So if you have a lens with 50mm diameter and you stop it down (reduce the surface area) to 25mm diameter then only one quarter of the light is passed through to the film.
If in the above example we were using a lens with 50mm focal length, considered the standard lens for a 35mm camera, and repeated the experiment with a telephoto lens of focal length 200mm then the result still holds true. However the amount of light captured by the telephoto lens will be much less than the standard lens if they both have the same diameter.
To demonstrate this form a circle with your forefinger and thumb and hold it before your eye. Then move it away from your eye and observe that the area captured within the circle diminishes.
If you consider an ideal scene which is uniformly illuminated then as the telephoto is gathering light from a much reduced area, then the amount of light falling on the sensor is less than the same scene using the standard lens.
However if the diameter of the lens is expressed as a fraction of the focal length, for example
25mm diam of 50mm focal length is 1/2 or f2
25mm diam of 100mm focal length is 1/4 or f4
Then the amount of light collected is proportional to the square of the f number. In the above case f4 gathers 1/4 as much light as f2
(22 /42) = 4/16 = 1/4
Whether digital sensor or film sensitivity is these days indicated by
its ISO rating. Lower the value lower the sensitivity.