Download Document

Electromagnetic Radiation
Cont….
Lecture 3
Dispersion of Radiation
If we look carefully at the equation ni =
c/vi and remember that the speed of
radiation in vacuum is constant and
independent on wavelength, and since
the velocity of radiation in medium i is
dependent on wavelength, therefore the
refractive index of a substance should
be dependent on wavelength. The
variation of the refractive index with
wavelength is called dispersion.
Refraction of Radiation
When a beam of radiation hits the
interface between two transparent
media that have different refractive
indices, the beam suffers an abrupt
change in direction or refraction. The
degree of refraction is quantitatively
shown by Snell's law where:
n1 sin 1 = n2 sin 2
Reflection of Radiation
An incident beam hitting transparent
surfaces (at right angles) with a
different refractive index will suffer
successive reflections. This means that
the intensity of emerging beam will
always be less than the incident beam.
Scattering of Radiation
When a beam of radiation hits a particle,
molecule, or aggregates of particles or
molecules, scattering occurs. The
intensity of scattered radiation is
directly proportional to particle size,
concentration, the square of the
polarizability of the molecule, as well as
the fourth power of the frequency of
incident beam. Scattered radiation can
be divided into three categories:
1. Rayleigh Scattering
Rayleigh Scattering is scattering of
electromagnetic radiation by particles
much smaller than the wavelength of the
radiation. Rayleigh Scattering usually
occurs in gasses. The scattering of solar
radiation by earth’s atmosphere is one of
the main reasons why the sky is blue.
Rayleigh Scattering has a strong
dependence on wavelength having a l-4
relationship.
2. Mie scattering
Mie scattering is caused
by dust, smoke, water
droplets, and other
particles in the lower
portion of the
atmosphere. It occurs
when the particles
causing the scattering
are close in dimension
to the wavelengths of
radiation in contact with
them. Mie scattering is
responsible for the
white appearance of the
clouds.
3. Tyndall Effect (nonspecific scattering)
It occurs in the lower portion of the
atmosphere when the particles are
much larger than the incident radiation.
This type of scattering is not
wavelength dependent and is the
primary cause of haze.
Quantum Mechanical Description of
Radiation
All the previously mentioned properties of radiation
agrees with the wave model of radiation. However,
some processes of interest to us, especially in this
course, can not be explained using the mentioned
wave properties of radiation. An example would be
the absorption and emission of radiation by atomic
and molecular species. Also, other phenomena
could not be explained by the wave model and
necessitated the suggestion that radiation have a
particle nature. The familiar experiment by Heinrich
Hertz in 1887 is the corner stone of the particle
nature of radiation and is called the photoelectric
effect.
The Photoelectric Effect
When Millikan used an experimental setup like
the one shown below to study the
photoelectric effect, he observed that
although the voltage difference between the
cathode and the anode was insufficient to
force a spark between the two electrodes, a
spark occurs readily when the surface of the
cathode was illuminated with light. Look
carefully at the experimental setup:
It is noteworthy to observe the following points:
1. The cathode was connected to the positive terminal
of the variable voltage source, where it is more
difficult to release electrons from cathode surface.
2. The anode was connected to the negative terminal of
the voltage source which makes it more difficult for
the electron to collide with the anode for the current
to pass.
3. The negative voltage was adjusted at a value
insufficient for current to flow. The negative voltage
at which the photocurrent is zero is called the
stopping voltage.
At these conditions, no current flows through
the circuit as no electrons are capable of
completing the circuit by transfer from
cathode to anode. However, upon
illumination of the cathode by radiation of
suitable frequency and intensity, an
instantaneous flow of current takes place. If
we look carefully at this phenomenon and try
to explain it using the wave model of
radiation, it would be obvious that none of
the wave characteristics (reflection,
refraction, interference, diffraction,
polarization, etc. ) can be responsible for this
type of behavior.
What actually happened during illumination is that
radiation offered enough energy for electrons to
overcome binding energy and thus be released. In
addition, radiation offered released electrons enough
kinetic energy to transfer to the anode surface and
overcome repulsion forces with the negative anode.
If the energy of the incident beam was calculated per
surface area of an electron, this energy is
infinitesimally small to be able to release electrons
rather than giving electrons enough kinetic energy.
When this experiment was repeated using different
frequencies and cathode coatings the following
observations were collected:
Conclusions
1. The photocurrent is directly proportional to
the intensity of incident radiation.
2. The magnitude of the stopping voltage
depends on both chemical composition of
cathode surface and frequency of incident
radiation.
3. The magnitude of the stopping voltage is
independent on the intensity of incident
radiation.