Page 20 - Modern Optical Engineering The Design of Optical Systems

Optics Overview 3

TABLE 1.1 Commonly Used Wavelength Units
Centimeter 10 2 meter
Millimeter 10 3 meter
Micrometer 10 6 meter 10 3 millimeter
Micron 10 6 meter 10 3 millimeter
Millimicron 10 3 micron 1.0 nanometer
10 6 millimeter
10 9 meter
Nanometer 10 9 meter 1.0 millimicron
Angstrom 10 10 meter 0.1 nanometer

The ordinary units of wavelength measure in the optical region are
the angstrom (Å); the millimicron (m ), or nanometer (nm); and the
micrometer ( m), or micron ( ). One micron is a millionth of a meter, a
millimicron is a thousandth of a micron, and an angstrom is one ten-
thousandth of a micron (see Table 1.1). Thus, 1.0 Å 0.1 nm 10 4 m.
The frequency equals the velocity c divided by the wavelength, and
the wavenumber is the reciprocal of the wavelength, with the usual
1
dimension of cm .

1.2 Light Wave Propagation
If we consider light waves radiating from a point source in a vacuum as
shown in Fig. 1.3, it is apparent that at a given instant each wave front
is spherical in shape, with the curvature (reciprocal of the radius)
decreasing as the wave front travels away from the point source. At a
sufficient distance from the source, the radius of the wave front may be
regarded as infinite. Such a wave front is called a plane wave.
The distance between successive waves is of course the wavelength
of the radiation. The velocity of propagation of light waves in vacuum
10
is approximately 3 10 cm/s. In other media the velocity is less than
in vacuum. In ordinary glass, for example, the velocity is about two-
thirds of the velocity in free space. The ratio of the velocity in vacuum
to the velocity in a medium is called the index of refraction of that
medium, denoted by the letter n.
velocity in vacuum
Index of refraction n
velocity in medium
wavelength in vacuum
(1.1)
wavelength in medium
Both wavelength and velocity are reduced by a factor of the index; the
frequency remains constant.