Equivalent focal length and aperture

Small mirrorless bodies with a sensor smaller than so-called full frame (135 format) are increasingly common. These are generally called crop-sensor cameras. The size difference between a full-frame sensor and a crop sensor is expressed as a crop factor — the diagonal of the larger sensor divided by that of the smaller one. When lenses made for crop-sensor cameras are discussed, the full-frame equivalent focal length is usually given. A 50 mm lens on a body with a crop factor of 2 has an equivalent focal length of 100 mm: the framing matches that of a 100 mm lens on a full-frame camera. What I do not recall ever seeing alongside such a focal-length comparison is the second half of it — the equivalent aperture, which depends on the crop factor in exactly the same way. At a factor of 2, f/4 corresponds to f/8. Yet advertising in particular often puts the equivalent focal length and the lens's true maximum aperture side by side, which is misleading. It is hard not to conclude that the intent is to make things look better than they are. Stating the equivalent focal length is genuinely useful if a photographer is used to thinking in full-frame terms — but then the aperture should be stated as an equivalent too. That would also help in judging depth of field, and at the very least it would not create false impressions.

I formed my own sense of how focal length, aperture, shutter speed, and film speed interact back in the last century, shooting a 35 mm film SLR. After moving to a Micro Four Thirds camera with a crop factor of 2, I sometimes wondered in low light why the shutter speed was not as short as I had expected from the ISO, aperture, and focal length I had chosen. The reason was simply that I was thinking of the focal length as the equivalent value while reading the aperture off the camera's viewfinder. So I imagined I was shooting at, say, an equivalent 100 mm at f/4, when I should have been imagining an equivalent 100 mm at f/8. Then the long shutter speed would not have surprised me. A photographer without these ingrained habits simply shoots a 50 mm lens at f/4 and thinks nothing of it.