Prism Dispersion Calculator
A prism disperses white light into a spectrum because the refractive index of glass varies with wavelength (shorter wavelengths refract more). At minimum deviation, the relationship between apex angle A, minimum deviation angle D, and refractive index n is: n = sin((A + D)/2) / sin(A/2). This calculator computes the minimum deviation angle from the apex angle and refractive index, and also estimates angular dispersion between two wavelengths given their refractive indices. The dispersion between two wavelengths is simply the difference in their deviation angles at minimum deviation.
Prism minimum deviation formula
n = sin((A + D) / 2) / sin(A / 2)
Solving for D: D = 2 arcsin(n sin(A/2)) - A
Where A is the prism apex angle and D is the minimum deviation angle, both in degrees. n is the refractive index at the wavelength of interest.
Dispersion and prism material selection
- Crown glass (BK7): n_d = 1.5168, Abbe number V approximately 64. Low dispersion, common for achromats.
- Flint glass (SF11): n_d = 1.7847, Abbe number V approximately 26. High dispersion, used to correct chromatic aberration in doublets.
- Fused silica: transparent from 185 nm to 2.1 um. Used for UV spectrometers.
- Dispersion increases at shorter wavelengths for all glass types, which is why prisms separate blue from red.
Prism dispersion: frequently asked questions
What is minimum deviation in a prism?
Minimum deviation (D_min) is the condition where light passes symmetrically through the prism (angle of refraction at each face is equal). At minimum deviation, n = sin((A + D_min)/2) / sin(A/2), where A is the apex angle and n is the refractive index. This is the standard method for accurately measuring refractive index.
How is angular dispersion calculated?
Angular dispersion is the change in deviation angle per unit change in wavelength: dD/dlambda = (dn/dlambda) x (2 sin(A/2)) / sqrt(1 - n^2 sin^2(A/2)). In practice, it is estimated from the difference in deviation angle for two wavelengths (e.g., the sodium D lines at 589 nm and the hydrogen F line at 486 nm).
What is the Abbe number?
The Abbe number V = (n_d - 1) / (n_F - n_C) characterizes the dispersion of optical glass, where n_d is the refractive index at 589 nm (sodium D line), n_F at 486 nm (hydrogen F line), and n_C at 656 nm (hydrogen C line). Lower Abbe number means higher dispersion. Crown glass has V around 60; flint glass around 35.
What materials are used for prism spectrometers?
Crown glass (n approximately 1.52 at 589 nm) is common for visible spectrometers. Flint glass (n approximately 1.62) has higher dispersion. For UV work, fused silica (quartz) is transparent down to 180 nm. For IR, germanium (n approximately 4.0) or zinc selenide is used.
What is the resolving power of a prism?
The resolving power of a prism is R = b x (dn/dlambda), where b is the base length of the prism and dn/dlambda is the dispersion of the prism material. A prism with a 50 mm base and glass with dn/dlambda = 1000 per meter at 589 nm can theoretically resolve wavelengths differing by 0.02 nm.
Official sources
- NIST, Optical Constants of Solids. physics.nist.gov.
- OpenStax University Physics Volume 3, Chapter 1: The Nature of Light. openstax.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.