Photography tips by Punit Sinha

Relationship between Aperture and Focal Length w.r.t Amount of Light

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The aperture of a lens is an opening through which light enters. Logically the larger the size of the aperture the more light will enter. To calculate the size of the aperture at a given fstop, we divide the focal length of the lens by the fstop number.

The aperture of a 80mm lens at f/8 will be a circle with diameter of 80/8 = 10mm

The aperture of a 32mm lens at f/8 will be a circle with diameter of 32/8 = 4mm

Does that mean that the 80mm lens is allowing more light than the 32mm lens at f/8? No. We have been rightly told that the light coming in at a given fstop is constant for all lenses of different focal length. Lets find out how.

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
             D is the distance and
             I is the Intensity

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) = 0.01227 .............. A

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) = 0.01227.............. B

We see that Equation A = Equation B

We can say that the amount of light coming in at f/8 is same across focal lengths.