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Crop Factor, Focal Length and Field of View
Posted By: Ole, 02-15-2010, 05:46 PM

Two of the most frequently asked questions are:

- what is the “crop factor”
- how does a full frame lens work when mounted on a DSLR with a 1.5 crop factor?

First, let's discuss focal length. We only discuss lenses with a positive focal length (converging lenses), i.e. such lenses as we use in photography.

When parallel light rays enter a lens, they will converge to a dot at a distance from the optical center of the lens. That distance is called the focal length, and the point where the light converges is the focal point. The focal length is usually denoted by the letter f.

From this definition we see that the focal length is a characteristic of a lens, it does not depend on the sensor size, and it does not change when the lens is mounted on differing camera bodies. As an example, an smc Pentax-A 50 mm lens is a 50 mm lens when mounted on a 24 x 36 mm "full frame" camera as well as when mounted on an APS-C body.

The focal length affects the field of view which the lens covers. A tele lens covers a narrow field of view (less of the subject gets recorded on the film/sensor) and has a longer focal length. A wide angle lens covers a wide field of view (more of the subject gets recorded on the film/sensor) and has a shorter focal length.

Now let's discuss crop factor and what happens when a lens is used on differently sized sensors.

The standard “full frame” format negative is 36mm on the longest side. The APS-C sensor which is used in Pentax DSLRS from the *istD series to the K series is 24mm on the longest side. The crop factor is 1.5, namely 36mm divided by 24mm.

Let's mount some lenses:

We mount the same lens with a focal length of f=50mm (say) on a full frame (24x36mm) camera (“A” above) and on an APS-C DSLR (“B” above).

We see that this same lens gives a narrower field of view on the APS-C DSLR than it does on the full frame camera (in actual numbers the horizontal field of view of a 50mm lens is 40 degrees on the 24x36mm format and just 27 degrees on the APS-C format (the illustration above is not to scale)).

If we want the same field of view on the APS-C DSLR as we have on the full frame camera then we need to use a lens with a shorter focal length on the APS-C DSLR (“C” above). We use the crop factor to determine the required focal length: f2 = f divided by the crop factor. In our example where we used a 50mm lens in illustration “A” we will need a 33mm lens (50 divided by 1.5) in illustration C.

In other words, a 50mm lens on a full frame sensor/film provides the same field of view as a 33mm lens on an APS-C sensor.

A handy table comparing Field of View across the many film/sensor formats in use in Pentax cameras is found here:

Last edited by Ole; 09-22-2011 at 08:06 PM.
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05-26-2013, 12:41 PM   #16
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Just remember that focal length is always the same measure. It has nothing to do with the sensor. A 50mm designed for Pentax film (135) has the same focal length as a 50mm lens designed for APS-C, which has the same focal length as a 50mm designed for MFT.

But the field of view will be different. And, as photographers, we care a lot about field of view since that is what is reflected in the final shot. With practice, you can tell FOV from looking at a photo. You cannot tell focal length from looking at a photo, unless you also know the sensor/film size.


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