How prisms work
A triangular prism, dispersing light; waves shown to illustrate the differing wavelengths of light. (Click to view animation)
Light changes speed as it moves from one medium to another (for example, from air into the glass of the prism). This speed change causes the light to be refracted and to enter the new medium at a different angle (Huygens principle). The degree of bending of the light's path depends on the angle that the incident beam of light makes with the surface, and on the ratio between the refractive indices of the two media (Snell's law). The refractive index of many materials (such as glass) varies with the wavelength or color of the light used, a phenomenon known as dispersion. This causes light of different colors to be refracted differently and to leave the prism at different angles, creating an effect similar to a rainbow. This can be used to separate a beam of white light into its constituent spectrum of colors. A similar separation happens with iridescent materials, such as a soap bubble. Prisms will generally disperse light over a much larger frequency bandwidth than diffraction gratings, making them useful for broad-spectrum spectroscopy. Furthermore, prisms do not suffer from complications arising from overlapping spectral orders, which all gratings have.
Prisms are sometimes used for the internal reflection at the surfaces rather than for dispersion. If light inside the prism hits one of the surfaces at a sufficiently steep angle, total internal reflection occurs and all of the light is reflected. This makes a prism a useful substitute for a mirror in some situations.
Deviation angle and dispersion
A ray trace through a prism with apex angle α. Regions 0, 1, and 2 have indices of refraction
, and primed angles
indicate the ray's angle after refraction.
Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface. For the prism shown at right, the indicated angles are given by
All angles are positive in the direction shown in the image. For a prism in air . Defining , the deviation angle is given by
If the angle of incidence and prism apex angle are both small, and if the angles are expressed in radians. This allows the nonlinear equation in the deviation angle to be approximated by
The deviation angle depends on wavelength through n, so for a thin prism the deviation angle varies with wavelength according to