Prisms are typically characterized by their angle of minimum deviation d. This minimum deviation is achieved by adjusting the incident angle until the ray passes through theprism parallel to the bottom of the prism. An interesting application of refraction of light in a prism occurs in atmospheric optics when tiny hexagonal ice crystals are in the air. This refraction produces the 22° halo commonly observed in northern latitudes. The fact that these ice crystals will preferentially orient themselves horizontally when falling produces a brighter part of the 22° halo horizontally to both sides of the sun; these bright spots are commonly called "sundogs". Calculation Polarizing prisms

How to calculateFOVmicroscope

An interesting application of refraction of light in a prism occurs in atmospheric optics when tiny hexagonal ice crystals are in the air. This refraction produces the 22° halo commonly observed in northern latitudes. The fact that these ice crystals will preferentially orient themselves horizontally when falling produces a brighter part of the 22° halo horizontally to both sides of the sun; these bright spots are commonly called "sundogs".

CalculateFOVfrom focal length

It is what Hermann said, focal length is NOT measured in pixels. I strongly doubt the engineering journal said focal length was pixels.

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As your sensor size is given in pixels (assumed square pixels!), your focal length will also be in pixels. To get it in a more usual unit (m), you need to know the pixel size.

The triangles (large and small) are similar, that is angles are the same. So Angle of view will be the same as top angle (at the lens) of the smaller triangle. From that, since you know what sensor size and angle of view is, you can calculate focal length in pixels, as @remco calculated for you.

FOVto focal length calculator

Fov calculationcalculator

It's basic geometry: you have a right angle triangle, with half the FOV as one of the angles (a), and half your image size as the opposite side (A). To calculate the focal length F, use tan(a) = A/F, which gives F = A/tan(a).

What you need to know for field of view is the camera sensor size (or film size) measured in mm. You must compute with sensor dimensions in mm.

Fov calculationcamera

There is a calculator that will do this at https://www.scantips.com/lights/fieldofview.html (Option 6). The geometry is shown at bottom of that page, however, you must use Trig for angles.

A refracting prism is a convenient geometry to illustrate dispersion and the use of the angle of minimum deviation provides a good way to measure the index of refraction of a material. Reflecting prisms are used for erecting or otherwise changing the orientation of an image and make use of total internal reflection instead of refraction.

Fov calculationonline

In fact, units of the sensor size should be exactly the same as units of the focal length to make sense of F=A/tan(a). What you can get from that is, if you have bigger pixels (in cm), you will need larger focal length (in cm) for same field of view and number of pixels.

The angle of minimum deviation for a prism may be calculated from the prism equation. Note from the illustration that this minimum deviation occurs when the path of the light inside the prism is parallel to the base of the prism. If the incident light beam is rotated in either direction, the deviation of the light from its incident path caused by refraction in the prism will be greater.

The article specifies that the horizontal FOV is 47°, so we have to use A = 640/2 = 320, a = 47°/2 = 23.5°, which give F = 736 pixels.