About crop factor:
You should know that the camera lens acts just like a slide projector lens. The camera lens projects a miniature image of the outside world on a flat screen. This screen is the surface of film or digital chip. Now most of you know that long focal length lenses magnify; they present a telescopic view, so we call them telephoto. Conversely, short focal length lenses yield a wide-angle view. Now you should ask yourself, what focal length when mounted on my camera yields a “normal” view? In the vernacular of photography, “normal” translates to a view that delivers about the same perspective as the unaided human eye.
Now over the years the size of the camera has shrunk. This is due to advancements in film and digital imaging sensors. Consider that the lenses used on the giant cameras of the past would perform as super telephoto lenses if mounted on today’s miniature cameras. So what constitutes a “normal” lens?
Every camera lens projects a large circular image. Inside the camera are baffles and a mask. These shunt the peripherals of the circular image area allowing only the central part of the image to play on film or sensor. We need this masking because only the center of the circular projected image has sufficient definition to be pictorially useful. For the full frame 35mm (Fx) format the size of the circle must be about 50mm. For the compact digital (Dx) format, the size of the circle must be about 30mm. These values are approximately the diagonal measurement of the image mask (film or digital format rectangle).
When we mount a lens with a focal length about the same as the diagonal measure, it delivers a circle of good definition that completely covers the format rectangle right down to the corners. In other words we get almost no fall-off of image quality over the entire span. Additionally, when we mount a lens with a focal length about equal to the diagonal measure of the format, we get an angle of view of about 45⁰ with the camera held in the horizontal (landscape) position. The image delivered by such a lash-up replicates the human perspective.
Now the full frame 35mm format stems from about the 1930’s. This frame size measure 24mm height by 36mm length. The “normal” lens for this rectangle is by tradition 50mm. The actual value is about 43mm but opticians prefer to round this value up to 50mm. The modern compact digital stems from advances in chip making. It measures 16mm height by 24mm length. Thus it is 66% of the size of the full frame. Now 66% = 0.66 expressed as a decimal fraction and the inverse of this value is 1/0.66 = 1.5. What is this value 1.5? It tells us that the Fx is 1.5 times larger than the Dx. How do we use this value? A 30mm lens mounted on a Dx preforms like a 30 x 1.5 = 45mm mounted on a Fx. Or a 105mm mounted on a Fx preforms like a 105 ÷ 1.5 = 70mm mounted on a Dx.
Is this crop factor (magnification factor) useful? Yes if you are an old gray-hair like me who has used full frame cameras for years and has lots of used but good lenses for them. For you youths, the crop factor is more confusing than useful. Know what’s wide-angle – normal – telephoto for your format Otherwise you will be more confused when tomorrows even smaller digitals hit the market. For the record: Wide-angle is 70% or normal or shorter – telephoto is 200% of normal or longer.