I don't know why this subject causes so much consternation every time it comes up; it's really just basic geometry. Well, OK, maybe that's why
To see the effect of crop factor, focal length, etc, it is useful to ask what one needs to do to take the same
image using different formats. This establishes a baseline; once you know what scaling of each image parameter is required to take the same image
, one can examine how the image will differ
when the parameters are changed away from those equivalent
Imagine taking a 35mm format camera/lens and shrinking everything by a factor of two in every linear dimension:
1. The sensor is now 18mm x 12 mm, the focal length is half, the aperture is half (so the f/ratio, which is the ratio of focal length/aperture diameter, remains the same). The angle of view remains the same -- we went wider in focal length but then cropped to a smaller portion of the image, and the two effects exactly compensate.
2. Because the f/ratio is the same, the physical depth of field of the image is the same. But the imager is twice smaller; we need the depth of field to be half of what it was in order to get the same image on our shrunken platform. Therefore we need to open up the aperture, and make the f/ratio half what it was for 35mm, so that the DoF is shrunk in the same proportion to the camera. In other words, objects at the edge of the DoF are focused a small distance in front or behind the sensor plane, and this distance should be shrunk by the same factor as the camera so that everything about the imaging process is in proportion to the smaller format.
3. If we want the same degree of motion blur in the image, we want objects that move across some angle relative to the angle of view during the exposure to traverse the same angle; since nothing has changed about the angle of view, using the same shutter speed will result in the same amount of motion blur.
4. With half the f/ratio and the same shutter speed, the sensor receives four times the light during the exposure; the ISO should be dropped by a factor of four to to keep the raw data in the same range of values (in particular to avoid blowing out highlights).
So, the same photo results on the half-size format using the same shutter speed, half the f/ratio, half the focal length and one quarter the ISO (if available). Change any one of these parameters, and a different image results. So for instance if one doesn't halve the f/ratio, the DoF will be deeper and the sensor receives less light, increasing the appearance of noise. Differences between the formats most often arise at the limits of the available range of parameters; for instance the 35mm format image taken at a base ISO of 100 will have no equivalent in the half-size format unless the camera goes down to ISO 25, which such cameras typically do not. And sufficiently wide angle, wide aperture lenses may not be available relative to their 35mm equivalents, etc.