What is “focal length magnification” and how does it work?

March 14, 2014 at 10:30 am  •  Posted in News & Events, Q&A, Tips & Techniques by

Recently, I read a few articles on the Internet about lenses and several mentioned “focal length magnification.” Others discussed the “crop factor” and several specified a “focal-length equivalent” for various lenses. What exactly does this all mean and why would a 300-mm f/4 lens be a 450-mm f/4 lens when using a Nikon D7100 versus a Nikon D610, for example?
—Billy L.

As you may recall, Billy, 35-mm cameras were the norm at one time and all models of all brands took photos on 24 x 36-mm frames of film. Eventually, digital SLRs became the norm. Some of the cameras (like the Nikon D610, but also some Canon and Sony models) use a so-called “full-frame” 24 x 36-mm sensor. When you mount that 300-mm lens on a full-frame DSLR it provides exactly the same effect you’d get if you were using a 35-mm film SLR.

While some cameras—such as the Nikon D610, EOS 5D Mk III, Sony a99 or a7R and others—employ a full-frame 24 x 36-mm sensor, a smaller chip is more commonly used in other DSLRs (and in compact-system cameras). This difference in the size of the capture medium is the reason for the so-called “crop factor” discussed in the text.

However, the majority of DSLR cameras of all brands employ a sensor that’s smaller than 24 x 36 mm. For example, the Nikon D7100 uses a 15.6 x 23.5-mm chip. (Nikon calls this the DX format vs. FX for full-frame.) When you mount that 300-mm lens on this type of camera, it still projects a large image circle but the smaller sensor cannot record the entire area. Hence, only part of the scene is actually captured. If you were taking a photo of an eagle, for example, some of its surroundings would be excluded (cropped). As a result, the photo would appear as if it had been made with a longer lens, because the eagle is larger in the frame than in a photo made with a full-frame DSLR.

More specifically, the photo of the eagle made with the D7100 (with the smaller sensor) would appear as if it were taken with a 450-mm lens on the (full-frame) D610. We often refer to this as a lens’ “focal-length equivalent” when used on a camera with a smaller sensor. However, some articles refer to the effect as a “focal-length magnification factor,” specifically 1.5x in this example. The terminology is inaccurate because nothing is actually magnified.

 

Photo A was made with a 200-mm lens on a full-frame Nikon DSLR, while Photo B shows the image that a DSLR with the smaller (DX) sensor would have provided. As this illustration confirms there's no difference in magnification, only in the field of view, which is cropped by a smaller sensor, making the subject appear to be larger. (Photo made in controlled conditions.) © 2012 Peter K. Burian

Photo A was made with a 200-mm lens on a full-frame Nikon DSLR, while Photo B shows the image that a DSLR with the smaller (DX) sensor would have provided. As this illustration confirms there’s no difference in magnification, only in the field of view, which is cropped by a smaller sensor, making the subject appear to be larger. (Photo made in controlled conditions.) © 2012 Peter K. Burian

A lens always projects the same field of view (picture coverage), but a smaller sensor records only part of it. Hence, you get a “field-of-view crop.” This is a more accurate term because it explains what really happens with a small sensor vs. a full-size sensor. And we then refer to a “crop factor” of 1.5x when discussing a lens used on camera with a 15.6 x 23.5-mm sensor instead of a 24 x 36-mm sensor. (This is also discussed in the previous Q & A “Should I buy a full-frame DSLR?”)

The sensors in DSLRs that are not full-frame vary in size depending on the brand of camera, so the “crop factor” also differs. It’s 1.5x with a Nikon, Sony or Pentax DSLR, but it’s 1.6x with a Canon EOS DSLR and 2x with an Olympus DSLR. The same concepts also apply to the mirrorless interchangeable-lens cameras (also called compact-system cameras). Some of these use even smaller sensors than DSLRs, so you’ll find an even greater variety of “crop factors.” While that may seem confusing at first, it all makes sense once you understand the basic concept.