Camera Lens Aperture

Camera lenses have a diaphragm (also called an aperture) which allows light to pass through

to the film. For example, in the figure above, the outer circle is the lens and the inner circles are the diaphragms. Note that the size (area) of the aperture can change. A larger aperture allows more light to pass through. The size of the aperture is determined by the f numbers (also called f stops). The size of the aperture and the f stops are inversely proportional. A typical 50 mm lens has the following f stops: f2.8, f4, f5.6, f8, f11, f16.

Inversely proportional relationships have a constant of proportionality. This constant is found from a combination of the size and f stop that works for all pairs of size and f stop. What is the constant of proportionality (approximate to the nearest integer) for the above relationship? How is it different from a proportional relationship? Can you create a similar problem to use with your students?

Extension:
What would you expect the constant of proportionality to be for a 200 mm lens? Explain.