Measuring Focal Length, Aperture and F-Stop

Measuring the aperture of a single element lens is even easier. Just measure the diameter of the lens, excluding any opaque border or mount. The f-stop (or the term I prefer: focal ratio) is simply the focal length divided by the aperture.

Example: Suppose that when you projected a distant light source through a lens and onto a piece of paper, the distance between the lens and the focused image was about 6 inches (150 mm). Suppose also that this lens is about 2 inches (50 mm) in diameter. The focal ratio of the lens is 6 divided by 2 (or 150 divided by 50) which equals f/ 3.0.

OK, that was too easy. Multi-element lenses are not that easy. First of all, you cannot determine the focal length of a multi-element lens simply by measuring the distance from the lens to a focused image. Doing that, doesn't tell you the focal length, however it does tell you something interesting. It tells you the back focal length, which is also important because that's where the film/sensor needs to be to capture focused images. But I'm getting off topic.

To understand the measurement of focal length, do the following experiment: Take that awful zoom kit lens that came with your camera (or any zoom lens), and starting with the lens set to its shortest focal length, measure the distance from the lens mount to a focused image just as we did above for a single element lens. If the lens was made for a SLR or DSLR, then you will get a measurement in the range of 45 mm. This is the back focal length. Now adjust the zoom to the maximum focal length and take the measurement again. What's this? It doesn't change. But did you notice that something else did change? The size of the image changed. So the key to measuring focal length of a complex lens is to measure the image size. It's possible to do this with an image projected on a piece of paper. But there's a better way: using photographs to compare the image size with a lens of a known focal length.

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