Page 47 - Optical Communications Essentials

The Behavior of Light

The Behavior of Light 37

Measurements in the EM Spectrum As can be seen from Fig. 1.7, there are three
different ways to measure various regions in the EM spectrum. These measurement
units are related by some simple equations. First, the speed of light c is equal to the
wavelength λ times the frequency ν, so that c λν. Rearranging this equation gives
the relationship between wavelength and frequency. For example, if the frequency is
known and we want to find the wavelength, then we use

8

c 310 m/s
λ (3.1)
ν ν
where the frequency ν is measured in cycles per second or hertz (Hz). Conversely, if the
wavelength is known and we want to find the frequency, then we use the relationship
ν c/λ.
The relationship between the energy of a photon and its frequency (or wavelength)
is determined by the equation known as Planck’s law
E hν (3.2)

where the parameter h 6.63 10 34 J s 4.14 eV s is called Planck’s constant. The
unit J means joules, and the unit eV stands for electron volts. In terms of wavelength
(measured in units of micrometers), the energy in electron volts is given by

1 2406
.
E eV (3.3)
λµ m

3.4. Refractive Index
A fundamental optical parameter of a material relates to how fast light travels
in it. Upon entering a dielectric or nonconducting medium, a light wave slows
down and now travels at a speed s, which is characteristic of the material and
is less than c. The ratio of the speed of light in a vacuum to that in matter is
known as the refractive index or index of refraction n of the material and is
given by

c
n (3.4)
s
Typical values of n to two decimal places are 1.00 for air, 1.33 for water, 1.45
for silica glass, and 2.42 for diamond. Note that if we have two different mate-
rials, then the one with the larger value of n is said to be optically denser than
the material with the lower value of n. For example, glass is optically denser
than air.

Number Accuracy People who design optical test and measurement equipment
often must know the precise value of the refractive index for air, and they need to take
into account its variation with wavelength, temperature, pressure, and gas composi-
tion. The wavelength dependence of the index of refraction n air of standard dry air at

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