f = 1 / (1/a + 1/b)

Measuring Focal Length, Aperture and F-Stop

I've been asked how I measure the focal length and f-stop of my homemade lenses. The answer is: That depends. It depends on whether I am measuring a single element lens, in which case there is a simple way to directly measure focal length and f-stop, or I am measuring a multi-element lens, in which case I use a comparison method. Let's take the simple case first.

Single element lenses with positive focal lengths, (that is, they focus light, rather than diverge it) can be directly measured to determine their focal lengths and apertures. You'll need a piece of paper, a ruler, and a distant light source such as a lamp across the room (do NOT use the sun for this). Project the light from the lamp through the lens and onto the paper. Adjust the distance between the lens and the paper until the image is at its sharpest. Now just measure the distance from the lens to the image on the paper. This is the focal length of the lens, or close to it. Ideally, the light source should be an infinite distance away, but I find that a light across the room gives me a pretty good approximation. (If you insist on precision, then also measure the distance from the object to the lens and use the formula given above.)

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