All lenses project a circular image but only the center portion of the circle is pictorially useful. Why is this? The light rays that play on the edges of the circle arrive at an angle. You can demonstrate this with a flashlight. Point the flashlight beam straight onto a piece of paper and you will see a brilliant sharply defined circle. Allow the flashlight to play on the paper at an angle and you will see an oval of light. It will make a weaker spot because the light must paint a larger surface area. Same with a lens, the edges of the image are weak and fuzzy. We call the center of the projected image, “the circle of good definition”.
We want to use only the circle of good definition because we will get a better picture. So we discard the periphery by baffle and mask inside the camera. The rectangular image area within this frame is a faithful image.
The focal length of the lens in millimeters tells how wide the angle-of-view will be and the size the image of objects will be. As a rule-of-thumb we mount a lens with a focal length about equal to the measure of the diagonal of the frame. For the 35mm frame these measurements are 24mm height by 36mm length. The diagonal of this rectangle is 43mm. Opticians round this up to 50mm and they generally fit a 50mm lens to the 35mm camera. By the way, 35mm refers to the width of the film. The image area is smaller because the film is punched on both sides with sprocket holes. The modern full frame digital camera adopts this image size.
If you mount a 50mm on a full frame camera (Fx) you get a “normal view”. Normal means the image obtained replicates the unaided human eye as to perspective. The angle of view delivered is 45⁰ with the camera held in the landscape orientation (horizontal). If you mount a shorter lens, the angle of view increases. The realm of wide-angle is considered to be 70% of normal which is 35mm or shorter. A telephoto lens is longer than normal, usually 200% which is 100mm or longer.
Now the venerable 35mm size has been with us for nearly 100 years. The size of frame is based on technology. In modern times we can use a smaller frame. One popular frame or format size is 66% of the full frame and we call it compact digital or Dx. This frame measures 16mm height by 24mm length. The diagonal of this rectangle is 30mm.
If we own a Dx, then a 30mm lens delivers a “normal” view. If we mount a lens 70% shorter = 20mm or shorter, the view is wide-angle. If we mount a lens 200% of normal = 30 x 2 = 60mm or longer we are in the realm of telephoto. No crop factor needed if you know the “normal” focal length.
Can we find a number or factor to compare Fx with Dx? We divide the 50 by 30 = 1.5. This is what we call a crop factor. It tells us if we mount a 50mm on an Dx it will deliver an angle of view that will be the same as a 50 x 1.5 = 70mm mounted on a Fx.
As to edge degrading: As a rule of thumb if we mount a lens that is equal to or greater than the diagonal measure of the format, we need not worry about any edge debasing. We call this vignetting. However a wide-angle lens is always shorter than the diagonal. How do we get away with this? The design of the lens is changed. Most times we use an inverted telephoto. This is like looking through binoculars backwards. Such a design delivers a wide-angle view without much vignette plus it places the rear element of the lens further away from the imaging chip. This extra clearance is needed in the DSLR to make room for the reflex mirror that sits between lens and imaging chip. This design is called a retro-focus.
Different crop factors are calculated if the image sensor is bigger or smaller. You might get 1.4 or 1.5 or 1.6 etc. I don’t like crop factors. I think they are confusing unless you are a gray-hair like me (77 years old) who is familiar with the angle-of-view of the old 35mm camera. If you never used this now ancient format, forget the crop factor.