In optics, a prism is a transparent optical element with flat, polished surfaces that
refract light. At least two of the flat surfaces must have an angle between them. The exact
angles between the surfaces depend on the application. The traditional geometrical shape
is that of a triangular prism with a triangular base and rectangular sides, and in colloquial
use "prism" usually refers to this type. Some types of optical prism are not in fact in
the shape of geometric prisms. Prisms can be made from any material that is transparent
to the wavelengths for which they are designed. Typical materials include glass, plastic and
fluorite. A dispersive prism can be used to break light
up into its constituent spectral colors. Furthermore, prisms can be used to reflect light, or to
split light into components with different polarizations.
How prisms work
Light changes speed as it moves from one medium to another. This speed change causes the light
to be refracted and to enter the new medium at a different angle. 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. The refractive index
of many materials 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. 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
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 .
Prisms and the nature of light
Before Isaac Newton, it was believed that white light was colorless, and that the prism
itself produced the color. Newton's experiments demonstrated that all the colors already existed
in the light in a heterogeneous fashion, and that "corpuscles" of light were fanned out
because particles with different colors traveled with different speeds through the prism. It
was only later that Young and Fresnel combined Newton's particle theory with Huygens' wave
theory to show that color is the visible manifestation of light's wavelength.
Newton arrived at his conclusion by passing the red color from one prism through a second
prism and found the color unchanged. From this, he concluded that the colors must already
be present in the incoming light — thus, the prism did not create colors, but merely
separated colors that are already there. He also used a lens and a second prism to recompose
the spectrum back into white light. This experiment has become a classic example of the methodology
introduced during the scientific revolution. The results of this experiment dramatically
transformed the field of metaphysics, leading to John Locke's primary vs secondary quality
distinction. Newton discussed prism dispersion in great
detail in his book Opticks. He also introduced the use of more than one prism to control
dispersion. Newton's description of his experiments on prism dispersion was qualitative, and is
quite readable. A quantitative description of multiple-prism dispersion was not needed
until multiple prism laser beam expanders were introduced in the 1980s.
Types of prisms Dispersive prisms
Dispersive prisms are used to break up light into its constituent spectral colors because
the refractive index depends on frequency; the white light entering the prism is a mixture
of different frequencies, each of which gets bent slightly differently. Blue light is slowed
down more than red light and will therefore be bent more than red light.
Triangular prism Abbe prism
Pellin–Broca prism Amici prism
Compound prism Grism, a dispersive prism with a diffraction
grating on its surface Reflective prisms
Reflective prisms are used to reflect light, in order to flip, invert, rotate, deviate
or displace the light beam. They are typically used to erect the image in binoculars or single-lens
reflex cameras – without the prisms the image would be upside down for the user. Many
reflective prisms use total internal reflection to achieve high reflectivity.
The most common reflective prisms are: Porro prism
Porro–Abbe prism Amici roof prism
Pentaprism and roof pentaprism Abbe–Koenig prism
Schmidt–Pechan prism Bauernfeind prism
Dove prism Retroreflector prism
Beam-splitting prisms Some reflective prisms are used for splitting
a beam into two or more beams: Beam splitter cube
Dichroic prism Polarizing prisms
There are also polarizing prisms which can split a beam of light into components of varying
polarization. These are typically made of a birefringent crystalline material.
Nicol prism Wollaston prism
Nomarski prism – a variant of the Wollaston prism with advantages in microscopy
Rochon prism Sénarmont prism
Glan–Foucault prism Glan–Taylor prism
Glan–Thompson prism Deflecting prisms
Wedge prisms are used to deflect a beam of light by a fixed angle. A pair of such prisms
can be used for beam steering; by rotating the prisms the beam can be deflected into
any desired angle within a conical "field of regard". The most commonly found implementation
is a Risley prism pair. Two wedge prisms can also be used as an anamorphic pair to change
the shape of a beam. This is used to make a round beam from the elliptical output of
a laser diode. Rhomboid prisms are used to laterally displace
a beam of light without inverting the image. Deck prisms were used on sailing ships to
bring daylight below deck, since candles and kerosene lamps are a fire hazard on wooden
ships. In optometry
By shifting corrective lenses off axis, images seen through them can be displaced in the
same way that a prism displaces images. Eye care professionals use prisms, as well as
lenses off axis, to treat various orthoptics problems:
Diplopia Positive and negative fusion problems
Positive relative accommodation and negative relative accommodation problems.
Prism spectacles with a single prism perform a relative displacement of the two eyes, thereby
correcting eso-, exo, hyper- or hypotropia. In contrast, spectacles with prisms of equal
power for both eyes, called yoked prisms shift the visual field of both eyes to the same
extent. See also
Minimum deviation Multiple-prism dispersion theory
Prism compressor Prism dioptre
Prism Theory of Colours
Triangular prism Superprism
Eyeglass prescription References
Further reading Hecht, Eugene. Optics. Pearson Education.
ISBN 0-8053-8566-5. External links
Java applet of refraction through a prism Grisms
Fundamental Optics – CVI Melles Griot