Geometric derivation

The focal length describes the distance between the focal point and the image plane, respectively in the drawing the distance between the magnifying glass (focal point) and the paper (image plane).

Geometric derivation

These distances can easily be geometrically defined with help of the diagonal of the field of view. Therefore the first thing we have to do is to calculate the diagonal.

Pythagoras' theoremHere we use Pythagoras' theorem:

The square root of (the length of the field of view squared plus the width of the field of image squared) yields the diagonal of the field of view.


b=diagonal of the field of view

To calculate the focal length, we need the half of the diagonal of the field of view (g), on which the focal length we want to calculate is perpendicularly “standing”, and the half of the aperture angle of the lens.
Now we use a trigonometrical function, the tangent.
The tangent of an angle is defined as the opposite leg (g) divided by the adjacent leg (a).

An example:

The viewing angle of an average human eye is approximately 47°. A lens, which represents this properties, is called a lens with standard focal length.

When using 35mm film format, the picture is distributed to a field of the dimensions 24 mm x 36 mm. For a 35mm film camera, this is achieved with a 50mm lens.

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