1.2.1 weave characterization of electro megnetic radiation

Wave characterisation of
electromagnetic radiation

COMPILED BY TANVEER AHMED 1

INTRO
• All electromagnetic radiation, including light,
travels through a vacuum with a velocity
• c of 3 X 10 8m s–1 (about 186 000 miles per
second).
• This value is constant for all types of radiation,
and whatever its intensity.
• When light has to travel through a medium of
refractive index n, however, its speed is given by
Eqn 1.1:


Wavelength
• Treating electromagnetic radiation as a
• transverse wave motion,
• the different forms can be distinguished by their
wavelength λ, defined in Figure 1.2 by the
distance AB.


Frequency
• An alternative parameter is the frequency v, defined as
• the number of complete waves from a single wave train
passing a given point in space in one second
• (the unit of frequency is known as the hertz and has
dimensions of s–1).
• Frequency is also measured as
• the reciprocal of the time taken for one wave to pass the
given point in space (the time period T of the radiation,
Figure 1.3) (Eqn 1.2):


The wavelength and
frequency of radiation are
related to its velocity by
Eqn 1.3:


Radiation in the UV and the visible regions of the electromagnetic
spectrum is usually
described in terms of its wavelength,

whereas in the IR both
wavelength units and
wavenumber units
are in common use.

wavenumber v – , which is the
number of wavelengths per metre, i.e. the
reciprocal of the wavelength (Eqn 1.4):


The unit of length
• The unit of length that is chosen for wavelength depends
largely on the region of
–the spectrum
• that is being studied.
• Thus yellow-green light near the centre of the visible spectrum
is said to have a
– wavelength of 550 nanometres
– (1 nm = 1 x 10 –9 m).
• This is preferable to describing the wavelength as
• 0.000, 000,550 m, which is cumbersome.
• Similarly we might describe radiation in the mid-IR range as
having a wavelength of 10 mm (or a wavenumber of 1000 cm–1)
rather than a wavelength of 10 000 nm or even 0.000, 01 m.

The usual rule is,
where possible, to choose a unit of wavelength
which keeps the numbers in the range 1 to 1000.


The visible region
• The visible region of the electromagnetic spectrum makes up a very
small part of
– the total spectrum
• Averaged visual assessments
• have placed a
• with no true red appearing in the spectrum (long-wave red has a
yellowish cast).

pure (or unitary) blue hue at 436 nm, pure green at 517 nm, pure yellow at 577 nm,

Energy content of
radiation

Many properties of light, particularly those relating to
absorption and emission of energy
by atoms and molecules,
cannot be fully explained by the wave theory of light.

QUANTUM THEORY
• The alternative (quantum) view that electromagnetic
radiation exists as a
• series of energy packets called photons
• is accepted as the best model for understanding the
energetics of the processes of light absorption and
emission.
The photon energy depends
• directly on the frequency of the radiation involved, as given
by Planck’s relationship (Eqn 1.5):

The energy given by Eqn 1.5 represents the small amount of
energy in a quantum of radiation, and is typically the amount of
energy absorbed by a single atom or molecule.

QUANTUM THEORY
• The equivalent amount of energy absorbed by a
mole of chemical material
• (assuming complete absorption at the frequency
or wavelength concerned)

• is obtained by multiplying the value of E in Eq 1.5
by Avogadro’s number (N = 6.023 X10 23).
• Suppose, for example, that a blue dye molecule
absorbs strongly at 600 nm in the orange/red
region.
• This corresponds to energy absorption Emol given
by Eqn 1.6:


QUANTUM THEORY
• or Emol = 199 409 joules per mole (about 200 kJ
mol –1).

This is a large amount of energy
• and can, in principle, lead to breakdown of
chemical bonds
• and destruction of the dye molecule.


Measurements of light
intensity
In order to quantify the amount of radiation
emitted by a source
and travelling through space
to fall on a surface,
we need to specifiy the radiation amount in different

Measurement of light intensity
• Our choice of unit depends on whether we
consider all the radiation emitted by the
• source, only that emitted
– in a certain direction
– (or over a certain solid angle),
– or that falling on a given area of the surface
• The familiar slide projector and screen set-up is a
good illustration of the quantities
• that need to be considered.
• We would first of all be interested in the
– total power emitted by the projector, which is
measured in watts.


• We can imagine the radiation as a
– series of particles or photons
– travelling between
– the light source and the screen
– And hitting the screen at a certain rate,

• that is, with a definite number of collisions per
• second (in wave terminology, we are considering
the amplitude of the wave here).

• The total radiant flux hitting the screen will be
measured in joules per second or in watts.


• The projector is designed,
– using mirrors and lenses,
– to throw the radiation
– in a certain direction
• so that what is important is that the radiant intensity or the
number of photons per unit solid angle per second (i.e.
the flux per unit solid angle) is reasonably
• constant over the illuminated screen area.

• If, however, the screen is moved closer to the projector
• the radiance or intensity per unit area increases,
• whilst if it is moved further away the radiance decreases,
even although the radiant intensity is constant by
definition.

• For a given distance of the screen we can
measure the

• irradiance or flux per unit area (in watts per
square metre, for example),

• and if we allow the radiation to fall
• on the screen for a known time
– we can then compute the total radiant exposure in
joules per square metre.


In this discussion we have considered the total radiant emission
which, for a typical projector,
will include both
visible (light)
and IR (heat) emissions.

In terms of viewing a projector screen what is important is the
overall effect on the human eye, which
means we should concern ourselves
with only the luminous radiation
and define appropriate quantities in terms of the visual
effect of the radiation.
Such terms and the relevant units are indicated in Table 1.1.


• The fundamental relationship between radiant and luminous quantities is
incorporated in the definition of
• the lumen, which is defined as the luminous
• flux of a beam of yellow-green monochromatic radiation
• whose frequency is 540 x 1012 Hz
• (equivalent to a wavelength of about 555 nm)
• and whose radiant flux is 1/683 W.

• The relationship is of course wavelength-dependent, since radiation
outside the visible spectrum has
– zero luminous contribution.
• The variation with wavelength is defined by the so-called Vλcurve,
• which has a maximum at 555 nm and decreases to zero at the ends
• of the visible spectrum.
• The use of Vλ values and their variation with wavelength are discussed
in section 1.6

1.2.1 weave characterization of electro megnetic radiation

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