Page 222 - Modern Optical Engineering The Design of Optical Systems

Chapter
10

Optical Materials

10.1 Reflection, Absorption, Dispersion
To be useful as an optical material, a substance must meet certain basic
requirements. It should be able to accept a smooth polish, be mechani-
cally and chemically stable, have a homogeneous index of refraction, be
free of undesirable artifacts, and of course transmit (or reflect) radiant
energy in the wavelength region in which it is to be used.
The two characteristics of an optical material which are of primary
interest to the optical engineer are its transmission and its index of
refraction, both of which vary with wavelength. The transmission of an
optical element must be considered as two separate effects. At the
boundary surface between two optical media, a fraction of the incident
light is reflected. For light normally incident on the boundary the frac-
tion is given by
(n′ n) 2
R (10.1)
(n′ n) 2
where n and n′ are the indices of the two media (a more complete
expression for Fresnel surface reflection is given in Chap. 11).
Within the optical element, some of the radiation may be absorbed
by the material. Assume that a 1-mm thickness of a filter material
transmits 25 percent of the incident radiation at a given wavelength
(excluding surface reflections). Then 2 mm will transmit 25 percent of
25 percent and 3 mm will transmit 0.25 0.25 0.25 1.56 percent.
Therefore, if t is the transmission of a unit thickness of material, the
transmission through a thickness of x units will be given by

T t x (10.2)

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