The 1.6x factor
Do APS-C crop-sensor cameras really multiply the focal length of your lenses?
One of the regular questions I receive is about the difference between full-frame and crop cameras with the same lenses. A lens has a fixed optical configuration, putting it on a full-frame or a crop camera makes no difference to its physical characteristics.
A full frame sensor is 36x24mm in size, so an EF lens needs to form a circular image at least 43.2mm in diameter to do this. APS-C sensors are 22.4x15mm in size. An attached EF lens still produces an image circle of 43.2mm, but only the central 27mm illuminates the sensor. This has the effect that smaller sensors appear to magnify the image, as if a longer focal length lens was used.
What is really happening is that the angle of view of the APS-C camera is narrower than the full-frame camera. As photographers we are accustomed to using the lens focal length as a means to quantify the angle of view. A 50mm standard lens should have a similar angle of view as regular human vision on a full-frame camera. However, that same lens on a smaller APS-C sensor has a narrower angle of view equivalent to a longer focal length on a full-frame sensor. The term ‘crop factor’ was coined to apply a simple multiplier to focal length that conveys this narrowing of the angle of view.
Canon APS-C sensors have a crop factor of 1.6x, so the 100mm lens on an APS-C sensor camera gives the same angle of view as a 160mm lens on a full-frame camera.
Smaller sensors allow manufacturers to make smaller cameras, with smaller mirror assemblies, shutter curtains, viewfinder pentaprisms and so on. All this contributes to lower costs, smaller sizes and lighter camera bodies. Likewise, lenses designed only for use on APS-C cameras can be made with smaller glass elements, making the lens smaller, lighter and cheaper.
The downside is that the smaller sensor area means the same number of pixels have to individually be smaller on an APS-C than a full-frame sensor. Smaller pixels are less sensitive to light.
In summary, the size of the sensor does not change the focal length of a lens, but it does change the angle of view. It is because we use focal length as a simple means to represent angle of view that the confusion arises.