lens - Why do Full Frame lenses and crop body lenses exhibit the same crop factor when used on a crop body camera?

I have a Canon 7D, which has a crop factor of 1.6x.

When using a Canon EF-S lens I get the focal length stated on the lens, when using a Canon EF lens I get the focal length times 1.6 when used on the APS-C body. At least that's what I thought.

I just compared two lenses:

• Canon EF-S 15-85mm f3.5-5.6


• Canon EF 70-200mm f4

I took the same photo as you can see here.

The top photo is shot with the 15-85, the bottom photo with the 70-200 - both lenses are set to 70mm. Now why do they look the same?

I thought I would get 112-320mm (70mm*1.6 crop factor). What did I misunderstand about the crop factor calculation? Lightroom also displays the photos as having "70mm" and not 112mm.

Answer

Whether a lens is an EF or an EF-S lens, the actual focal length is always used. There are certain technical reasons why this is so, but the simplest is that a lens' focal length is defined as the distance from the film plane needed when the lens is focused at infinity to cast point light sources as a single point on the film plane. This doesn't change with regard to sensor size. What does change with regard to sensor size is the angle of view or field of view (FoV) that a lens of a specific focal length will include in the part of the image circle that falls on the sensor.

What this means is that if you are using a 70mm lens on a Full Frame camera, the FoV will be about 34° diagonally. The same 70mm lens on a crop sensor body will have an FoV of about 21°. That is an equivalent FoV of about a 110mm lens on the FF body, and that is why camera manufacturers say that the 70mm lens on a crop body is a 110mm equivalent. If you print photos taken of the same subject from the same distance using the same focal length lens with both cameras on the same size paper, the image from the crop sensor camera will make the subject appear larger. This is because the ratio between the crop sensor size and the print size is greater than the ratio between the larger full frame sensor and the same print size, thus the magnification factor of the photo taken with the crop sensor body is higher.

If you take both images shot at 70mm on your 7D with an EF 70-200mm f/4L and an EF-S 15-85mm f/3.5-5.6 IS they will have the same FoV because both lenses are set at 70mm. To understand the 35mm equivalent FoV they yield, both lenses need to be multiplied by the crop factor, even though one of the lenses does not project a light circle large enough to fill a full frame sensor.