Dispersive prism

Photograph of a triangular prism, dispersing light
Lamps as seen through a prism

In optics, a dispersive prism is an optical prism, usually having the shape of a geometrical triangular prism, used as a spectroscopic component. Spectral dispersion is the best known property of optical prisms, although not the most frequent purpose of using optical prisms in practice. Triangular prisms are used to disperse light, that is, to break light up into its spectral components (the colors of the rainbow). Different wavelengths (colors) of light will be deflected by the prism at different angles, producing a spectrum on a detector (or seen through an eyepiece). This is a result of the prism's material (often, but not always, a glass) index of refraction varying with wavelength. By application of Snell's law, one can see that as the wavelength changes, and the refractive index changes, the deflection angle of a light beam will change, separating the colors (wavelength components) of the light spatially. Generally, longer wavelengths (red) thereby undergo a smaller deviation than shorter wavelengths (blue) where the refractive index is larger.

A good mathematical description of single-prism dispersion is given by Born and Wolf.[1] The case of multiple-prism dispersion is treated by Duarte.[2]

The dispersion of white light into colors by a prism led Sir Isaac Newton to conclude that light consisted of a mixture of different colors, which when combined could appear "white."

Overview

Although the refractive index is dependent on the wavelength in every material, some materials have a much more powerful wavelength dependence (are much more dispersive) than others. Crown glasses such as BK7 have a relatively small dispersion, while flint glasses have a much stronger dispersion (for visible light) and hence are more suitable for use as dispersive prisms. Fused quartz and other optical materials are used at ultraviolet and infrared wavelengths where normal glasses become opaque.

The top angle of the prism (the angle of the edge between the input and output faces) can be widened to increase the spectral dispersion. However it is often chosen so that both the incoming and outgoing light rays hit the surface at around the Brewster angle; beyond the Brewster angle reflection losses increase greatly. Most frequently, dispersive prisms are equilateral (apex angle of 60 degrees) where this is approximately the case.

Types

Types of dispersive prism include:

Grating and prism mountings

There are six grating/prism configurations which are considered to be "classics":[3]

  • Paschen-Runge
  • Eagle
  • Wadsworth
  • Ebert-Fasti
  • Littrow
  • Pfund

Grisms (grating prisms)

A diffraction grating may be ruled onto one face of a prism to form an element called a "grism". Spectrographs are extensively used in astronomy to observe the spectra of stars and other astronomical objects. Insertion of a grism in the collimated beam of an astronomical imager transforms that camera into a spectrometer, since the beam still continues in approximately the same direction when passing through it. The deflection of the prism is constrained to exactly cancel the deflection due to the diffraction grating at the spectrometer's central wavelength.

A different sort of spectrometer component called an immersed grating also consists of a prism with a diffraction grating ruled on one surface. However in this case the grating is used in reflection, with light hitting the grating from inside the prism before being totally internally reflected back into the prism (and leaving from a different face). The reduction of the light's wavelength inside the prism results in an increase of the resulting spectral resolution by the ratio of the prism's refractive index to that of air.

With either a grism or immersed grating, the primary source of spectral dispersion is the grating. Any effect due to chromatic dispersion from the prism itself is incidental, as opposed to actual prism-based spectrometers.

An artist's rendition of a dispersive prism is seen on the cover of Pink Floyd's The Dark Side of the Moon, one of the best-selling albums of all time. The iconic graphic shows a coherent ray of white light entering the prism and beginning to disperse, and shows the spectrum leaving the prism.

See also

References

  1. ↑ M. Born and E. Wolf, Principles of Optics, 7 ed. (Cambridge University, Cambridge, 1999), pp. 190–193.
  2. ↑ F. J. Duarte, Tunable Laser Optics (Elsevier Academic, New York, 2003).
  3. ↑ George J . Zissis (1995). "Dispersive prisms and gratings" (pdf) in Michael Bass et al. (eds.) Handbook of Optics. Vol. 2, Ch. 5. McGraw Hill.
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