Camera Sensor Size & Crop Factor
This short video graphically demonstrates the consequences of exchanging lenses (assuming compatible physical mounting systems) between cameras with image sensors of different sizes. This is often referred to as "crop factor."
The two theoretical cameras represented here have two common and popular sensor sizes: a 36mm x 24mm "full frame" sensor, and a smaller 22.2mm x 14.8mm "APS-C sensor. 50mm is a traditional standard for a "normal" lens - considered to have a field of view and image geometry similar to human vision. I've created a hypothetical 31mm lens for the APS-C camera to produce an identical image on the smaller sensor. So each lens - designed for their respective sensor sizes - gather light from exactly the same part of the scene, but project and focus this image onto different sized areas.
When the lenses are traded between the two camera bodies (this assumes that the bodies and lenses have a compatible physical "mount" system), their respective projected areas no longer match the sensors' areas. The 31mm lens' projected image of the scene falls short of filling the full-frame sensor, creating a recorded image that may appear undesireable, where the image is partially vignetted on the left and right sides by a soft circular pattern (which is actually the edge of circular lenses in the lens assembly). However, this may yield a usable image with a wider field of view than the 31mm "normal" lens which simply requires some cropping to be suitable for use. The 50mm lens' projection extends far beyond the edges of the APS-C sensors borders, and the sensor records a "cropped" inset - essentially as would a 50mm lens designed for an APS-C sensor, except that some gathered light is wasted off the edges of the sensor.
A photographer may be able to take advantage of understanding these behaviors to better utilize their existing collection of lenses or when presented with the opportunity to acquire new lenses. I use K-mount lenses from our old Pentax 35mm film SLR ("full-frame" digital sensors are the same size as the projected area on 35mm film cameras) on our APS-C sensor Pentax, where they behave like lenses longer than originally designed. For those familiar with the field of view produced by focal lengths for 35mm film cameras, it is helpful to establish a simple mathematical relationship which represents the comparitive sizes of the sensors which are involved. In our example here, dividing the one of the dimensions of the lens' projected area ("full frame" height = 24mm) by the same dimension of the camera sensor (APS-C height = 14.8mm) results in a focal length multiplier: 1.62 (24 ÷ 14.8). So our old 28-105mm Vivitar Series 1 lens produces the field of view as would have a 45-169mm lens (on 35mm film cameras) when mounted on our APS-C camera.