Everybody knows the meaning of Aperture and Focal Length. While a 50 mm lens is the normal human eye perspective, a lens with focal length of less than 50mm is known as wide angle and a lens with focal length of more than 50 mm is known as telephoto lens.

We know that f/8 or any fstop for that matter will allow the same amount of light coming it. We also know that f/8 means an aperture whose diameter is f divided 8 where f is the focal length of the lens in use.

Consider a 32-80mm wide angle telephoto zoom lens.

Lets see what happens to the aperture at f/8.

The size of aperture at 32mm will be a circle with diameter of 4mm at f/8.
The size of aperture at 80mm will be a circle with diameter of 10mm at f/8.

We see that the size of the aperture is not the same. Yet we say that the amount of light coming in at f/8 is same. The explanation is very simple. The lens at 80mm is longer than the lens at 32mm. Light falls in intensity over the distance it travels. So the light at the end of a longer lens is less intense than at the end of a shorter lens. Hence, for a 80 mm lens, if the size of the aperture is larger as compared to the 32mm lens, the amount of light coming in will be the same.

Mathematically:

The inverse sq law states:

“The intensity of the light is inversely proportional to the Sq of the distance it travels.”

      That is I is proportional to 1/(D * D) where
            I is the Intensity and
            D is the distance.

        For a 32mm lens at f/8
            Diameter is 32/8 = 4 mm, therefore radius = 2mm
            The area of the aperture is then 2 * 2 * pi = 4pi
            The focal length of the lens is 32mm so the intensity of the light
            = 4pi/(32 * 32) ..................... A
            = 0.01227

        For a 80mm lens at f/8
            Diameter is 80/8 = 10 mm, therefore radius = 5mm
            The area of the aperture is then 5 * 5 * pi = 25pi
            The focal length of the lens is 80mm so the intensity of the light
            = 25pi/(80 * 80) ..................... B
            = 0.01227

We see that Equation A = Equation B

Therefore, we can say that the amount of light coming in at f/8 is the same for all focal lengths.