Light as a Wave
The classical description of light as an electromagnetic wave makes
some assumptions about its nature, based on what could be observed at
the time. Although some of these assumptions have proven to be less than
accurate as we learn more about electromagnetic phenomena, they make a
good starting point for our discussion about light in particular and
electromagnetic waves in general. The two basic assumptions were:
- The frequency of the electromagnetic wave can be varied over the
entire positive range, but cannot be reduced to zero.
This seems intuitively obvious. A frequency of zero would mean no
change in the strengths of the electric and magnetic fields, but an
electromagnetic wave requires these fields to be constantly changing in
order to exist and the idea of a negative frequency seems ludicrous.
- The energy in the wave is continuously variable, with a minimum
energy of any non-zero value, and no maximum value.
This also seems intuitive. Looking at sunlight and comparing light
intensity on a clear day and a cloudy day, we note that the clouds block
some of the sun's energy. The desert sun at Noon is very intense, while
the setting sun at extreme northern or southern latitudes is much less
noticeable. Yet it is the same sunlight, coming from the same source, so
we know that various factors encountered by sunlight must be removing some
of the energy from it. We can see, feel, and scientifically measure the
difference.
Of course, other properties of electromagnetic radiation have also been
determined, and a number of theories and assumptions have been developed.
These have been either confirmed or disproven by experiment. Before we
look at the circumstances under which the wave model of light (or any
electromagnetic wave) may break down, however, let's look at the wave
model itself.
Since light was first recognized scientifically as a manifestation of
electromagnetic energy, it has been represented as a waveform, like
this:
If we think of this figure as representing the electrical energy
present in the light waveform as it travels from left to right,
it looks as if the energy level is becoming alternately positive and
negative, with momentary crossovers of zero electrical energy. In the
basic model of light shown here, this is in fact the case; as with all
electromagnetic waves, light energy is constantly changing its form
between electrical energy and magnetic energy. The point of maximum
magnetic energy coincides with the moment of zero electrical energy.
Beyond that instant, energy shifts again from the magnetic field back into
the electrical field, but with a reversal from the previous polarity. This
continues as long as that particular ray of light exists.
There are other "modes" of propagation which involve more complex
interactions between the electric and magnetic fields, but in all cases
the Law of Conservation necessarily holds true: Energy is neither created
nor destroyed as it is transformed from one form to another; the total
energy in the wave must somehow remain constant throughout the full
cycle.
NOTE: The sine wave shown here represents the strength and
polarity of the electrical and magnetic fields associated with the motion of this ray of
light. The light itself, assuming no outside influences, travels in a
straight line. The light energy does not "wiggle" back and forth
as it moves along its path.
As an electromagnetic wave, light has some characteristics in common
with all forms of electromagnetic energy. These include wavelength,
frequency, and speed of propagation. These characteristics
are actually related to each other, so that any one can be calculated if
the other two are known. Let's take a look at each of these
characteristics as depicted in the figure below:
Wavelength
Since light is a repeating waveform in motion, it is
possible to measure the physical distance between matching points of adjacent cycles of the waveform.
The symbol used to represent this distance is the Greek letter "Lambda" ( ).
The wavelength can actually be measured between any two corresponding
points on the waveform. It is convenient to use the most positive point or
the most negative point, both of which are shown above. However, we can
just as easily specify two zero-crossing points, so long as both
crossed the zero line in the same direction.
Remember that the light itself does not wave back and forth along its
path of travel. What we are actually measuring here is the distance
traveled through space by this ray of light, while its electrical field
goes from its maximum positive value, through zero to its maximum negative
value, and then through zero again to once more reach its maximum positive
value.
This distance is normally measured in meters (m) or some decimal
fraction of a meter, such as centimeters (cm). The correct units of
measurement are meters per cycle (m/cycle) or some appropriate derivation.
In the case of light, the wavelength is so short that a specific distance,
called the ångstrom (Å), has been defined.
One ångstrom = 10-10 m or 10-8 cm.
Visible light has a characteristic wavelength in the range of
approximately 3900 Å to 7700 Å. Electromagnetic energy outside
this range is no longer visible to the human eye.
Speed of Propagation
The speed at which light travels through any medium is
determined by the optical density of that medium. The presence of matter, even
transparent matter, will slow the light down. Even air will have some
effect, and glass has a more significant effect on the speed at which
light will travel through it.
Ever more sophisticated experiments have determined the speed of light
quite accurately. According to current knowledge:
Speed of light in a vacuum = 2.997925 ± 0.000002 x 1010
cm/sec.
As made famous in Einstein's equation, the letter c is used as a
general symbol for the speed of light.
Frequency and Period
In any electromagnetic wave, it takes time for the energy
in the wave to change from electrical format to magnetic and then back
again. The amount of time required to do this twice, covering one complete
cycle, or wavelength of the signal is known as the period of the
wave. Thus, the period of any wave, measured as some amount of time per
cycle, is in fact the time interval that corresponds to the physical
wavelength of the signal.
The frequency of the wave is the inverse or reciprocal of the
period. That is, the frequency is the number of cycles of the waveform
that occur in one second of time. For many years this was simply measured
in units of cycles per second. Recently, however, the specific name
hertz (abbreviated Hz) has been designated as the appropriate unit
to indicate cycles per second.
In general equations, the letter f is used to indicate frequency
in hertz.
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The basic mathmatical formula that relates wavelength, frequency, and
the speed of light is:
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c = f
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Wave Properties of Light
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