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Aperture angle

Angle that the lens can see in the direction of a given sensor measure.

The angles in horizontal, diagonal and vertical directions differ.
Please distinguish between the max. possible aperture angle and the actual aperture angle.
Actual aperture angles are influenced by the length of used extension rings,and even focus distances (because they are mostly achieved by simulating extension rings) max possible aperture angles aren’t
Changing the sensor size changes the actual aperture angle, max possible aperture angles aren’t
Datasheets of lenses usually show aperture angles for a given sensor size! Changing the sensor size changes the angles!
For lenses without distortion a lens that has the diagonal of the sensor as focal length has 53.1 degrees
A (no distortion) 6mm lens on a 1/3″ sensor,a 8mm lens on a 1/2″ sensor and a 16mm lens on a 1″ sensor have the same diagonal aperture angle of 53.1 degrees

aperture value

Number which characterizes the luminous sensitivity of a lens. Another term for aperture value is F-number.

Aperture Values

The smaller the number, the more light a lens can collect, the brighter the image, the smaller the depth of field.

The larger the number, the darker the image, but in generally the greater depth of field. At the same time, we generally lose resolution, see Rayleigh Criterion.

The f-number is the ratio of the focal length divided by the apparent size of the aperture (= entrance pupil diameter).

An f = 50mm lens with an F-number of F2.0  has to have least one front lens of \frac{50mm}{2.0} = 25mm diameter.
A lens with a focal length of f = 75, diameter 30mm and an F-number of F1.0  can’t exist!

The inverse of the square of the f-number is a measure for the image brightness of a lens.

The image through a F4.0 lens only has a quarter of the brightness of an F2.0 lens, since \frac{1}{4 * 4} four times smaller than \frac{1}{2 * 2}.
The image through a F5.6 lens has about twice the brightness of an image through an F8 lens, since \frac{1}{5.6 * 5.6} = \frac{1}{31.36} and \frac{1}{8 * 8} = \frac{1}{64}