# focal length

The focal length is the distance from the Image side principal plane to the image of objects at infinity.

For single lenses in air that is equal to the distance from the first focal point to the first principal point.
(in each case measured from the left to the right)

Note that this is a positive value for converging lenses and a negative value for the divergent lenses.

The larger the focal length, the smaller the aperture angle of the lens and the smaller the object section that is displayed full-frame on the sensor.
The lens captures less of the object. Extremea are telephoto lenses and finally telescopes.

The smaller the focal length, the larger the aperture angle of the lens and the larger the object section which is displayed full-frame on the sensor.
The lens captures more of the object. Extreme forms are fisheye lenses.

Lenses are typically listed, sorted by focal length. As an approximation, lenses with larger focal length see a smaller portion of the object (in more detail).

There are exceptions! (See: pseudo-knowledge: viewing angle and focal length are equivalent)

The following calculator determines focal length from angles.
However, Viewing angles change with the working distance! Also, a Pinhole lens model is assumed. Thus for wide angles a too small focal length is returned .. (as all focal length calculators on the internet do 😉 )

For the next calculator it is very important to correct the distortions before doing the calculation:

# focal point

Each (rotation symmetric) lens has two focal points on it’s optical axis.
They’re located where images of infinite distanct objects are generated.
The focal points belong to the Gauss-points.

When a ray of light is sent parallel to the optical axis into a lens or lens system, then the ray or it’s prolongation intersects the optical axis after exiting the last lens.

This intersection with the optical axis is called focal point.

The name is derived from “burning glasses” (imagine a magnifying glass) with which the (nearly parallel) sun beams are bundled to one point.
At this point it gets so hot that wood or paper placed at this spot starts to burn.