How is the crop factor, sometimes called magnification calculated?
The size of image sensor or film, in the jargon of photography, is called the “format”. For every format there is a focal length that delivers what is called the “normal” perspective. By normal we are taking about a perspective that replicates human vision. A “normal” perspective is achieved when we mount a lens with a focal length that approximately matches the diagonal measure of the film or image sensor frame.
As an example; the full frame (Fx) format measures 24mm height by 36mm length. The diagonal of this rectangle measures 43.27mm. If we mount a lens with this focal length the resulting image replicates the “human perspective”.
Technically the angle of such a lash-up view will be about 45⁰, camera is held in the horizontal (landscape) position.
Now the camera industry rounds the “normal” focal length for the 35mm full frame up to 50mm. This tradition started about 100 years ago with the introduction of the first 35mm, the Leica.
If a 50mm is considered “normal” for the Fx, what is wide-angle and what is telephoto?
As a rule of thumb a lens 70% of normal or shorter falls in the realm of wide-angle. Thus 50 x 0.7 = 35mm.
A lens 35mm or shorter is considered wide-angle for the Fx.
Telephoto is 200% or longer. Thus 50 x 2 = 100mm or longer is the realm of telephoto for the Fx.
Now your Sony sports a miniature sensor. The Sony’s imaging chip measures 8.8mm height by 13.2mm length. The diagonal measure of this format is 16mm.
How can we compare lenses between these two different frame sizes (Full frame vs. your camera)? We divide diagonals and the result is a crop or magnification factor. Correct is 43.27 / 16 = 2.7. This is the crop factor of your Sony.
What is the value of this number? Old gray hairs like me (77 years old) know the full frame and its lenses as to their angle of view. If you have never used a full frame than the only value will be -- you have lots of used but good lenses for the full frame on your shelf and you want to use them. Otherwise -- not much value. I think.
How do we use this crop factor? Mount a 50mm lens on the Sony RX100 and the 50mm projects an image of the Sony’s smaller sensor. The smaller sensor can only see the center area of image presented by this lash-up. How will the Sony RX100 preform with a 50mm. The view will be 50mm x 2.7= 135mm.
In other words if you mount a 135mm lens on a Fx, the view delivered will be about the same as a 50mm mounted on the Sony RX100. This is because the smaller sensor of the Sony RX100 can only view the central portion of the 50mm lens. The peripheral of the image formed by the 50mm is lopped off (cropped).
How do we figure “normal” perspective?
If we stand before a glass window and gaze at a vista, we can trace the outlies of objects on the glass with wax pencil. Such a drawing is made to the natural or “human” perspective. Can we duplicate this human perspective with the camera? Yes if we follow these rules.
- The camera replaces the human eye as to distance to the glass window.
- An image is taken (focal length not a factor).
- A contact print is made from this image.
- The image is viewed from a distance equal to the focal length of the camera lens. The image matches the “human perspective”
- The image is enlarged and viewed from a distance. A lens used about equal to the diagonal of the format. Most photographs are viewed from a distance about equal to the diagonal measure of the pictures dimension. The math as to what lens delivers a “normal” view, takes into account the degree of enlargement and the viewing distance
Today’s miniature cameras make a tiny image that is nearly useless unless magnified. We shoot with a full frame with a 50mm; we make an 8x12. The magnification applied is about 8X. The diagonal of the 8x12 is 14 inches (350mm. We tend to view from this distance.
If we make a 16 x24 from a full frame and a 50mm lens is used: This large print will likely be viewed from about 40 inches, (the diagonal). The magnification to make is about 20x; 50mm x 20 = 1000mm or about a meter (about 40 inches). The image is seen to have a “normal perspective.
We are taking a rule-of-thumb and not a law engraved in stone. Most images are viewed as OK even if the we violate this rule of thumb. An exception is the portrait. Too short or too long a lens and the image violates this rule and people say I don’t photograph well. The portrait is best when the lens used is about 2x thru 2.5x the focal length. Such a combination presents an image naturally viewed from a distance that replicates the human perspective.