such as reflection and refraction to be analyzed by the simple geometrical process of
ray tracing. This view of optics is referred to asray opticsorgeometrical optics.
The concept of light rays is very useful because the rays show the direction of
energyflow in the light beam.
To help understand wave optics, this sectionfirst discusses some fundamental
characteristics of waveforms. For mathematical convenience in describing the
characteristics of light,first it is assumed that the light comes from an ideal
monochromatic (single-wavelength) source with the emitted lightwave being rep-
resented in the time domain by an infinitely long, single-frequency sinusoidal wave,
as Fig.2.2shows. In a real lightwave or in an optical pulse offinite time duration,
the waveform has an arbitrary time dependence and thus is polychromatic.
However, although the waveform describing a polychromatic wave is nonharmonic
in time, it may be represented by a superposition of monochromatic harmonic
functions.
2.1.1 Monochromatic Waves
A monochromatic lightwave can be represented by a real waveform u(r, t) that
varies harmonically in time
uðÞ¼r;t AðÞr cos½xtþuðrÞ ð 2 : 1 Þwhereris a position vector so that
A(r) is the wave amplitude at positionr
φ(r) is the phase of the wave at positionr
ω=2πνis the angular frequency measured in radians/s or s−^1
λis the wavelength of the wave
ν=c/λis the lightwave frequency measured in cycles/s or Hz
T=1/ν=2π/ωis the wave period in units of seconds
Wavelength λ
or period TAmplitude A
Distance or timeFig. 2.2 A monochromatic
wave consists of a sine wave
of infinite extent with
amplitude A, wavelengthλ,
and period T
2.1 Lightwave Characteristics 27