Prism calculator

may 2017, Jeroen Korterik - University of Twente

Definition of the variables

Refer to the picture below;
i:the incoming angle with respect to the normal of the entrance surface
A:the top angle of the prism
r:the exit angle with respect to the normal of the exit surface
n1:the refractive index outside of the prism; typically, this is air -> n1=1.0
n2:the refractive index of the prism material

prism with light rays and angles indicated
In a normal situation e.g. a glass prism surrounded by air, this n2 is responsible for the dispersion of white light into the separate colors as n2 depends on the wavelength of the light. Strictly speaking, we should say 'n2 depends on the frequency of the light' as the wavelength depends on it's turn on the refractive index... However, refractive index vs. wavelength is used in practice where wavelength is the wavelength in air (or vacuum).
Refer to for instance https://refractiveindex.info/ for refractive index vs. wavelength plots of different types of 'glass'.

Calculator

angle i:
 [deg]
angle A:
 [deg]
n1:
n2:
angle r:
 [deg]
angle i with respect to the horizontal:
 [deg]
angle r with respect to the horizontal:
 [deg]
angle r with respect to the incoming ray:
 [deg]

Calculation method:

Snell's law
The incoming angle i (with respect to the normal of the entrance surface) is used in Snell's law to calculate the angle inside the prism (with respect to the same normal):
Next, this angle is calculated with respect to the normal of the exiting surface and Snell's law is applied again to calculate the angle r with respect to the exiting normal.
Both angles i and r are calculated as well with respect to the horizontal plane - the base of the pyramid.