A Look at the Transmission of Light Through Dense Media
When a beam of light enters a transparent material, the light will
interact with the atoms that make up the glass, plastic, water or
whatever media it happens to be. Everything is made up of
molecules. Air or the earth's atmosphere can be broken down into
little cubes that contain many molecules. Whatever number of molecules
are consituted within that will determine the optical density of the
material. All of these molecules are usually placed so closely
together that they are no longer considered random but are instead
considered to be a uniform substance. As wavelets of light pass
through this, there will be interference both constructively and
destructively. So many molecules placed together in such small areas
will mean that there is interence in all direction. In general, the
more molecules there are, the less scattering there will be. This is
why liquids in general scatter less than gases. Solids such as glass
and plastic do scatter but it is not as strong.
In all these molecules there are atoms which consist of electrons. The
particular index of refraction of the material will depend on the
specific arrangement of these atoms and the distribution of the
electrons. When these electrons are illuminated by light they will
move up and down because this light ray is an electromagnetic wave. An
electromagnetic wave is produced by vibrating electric charges. When
the wave moves through a vacuum and doesn't encounter any other
electromagnetic waves or charges it will move at the speed of c which
is 3.00 e.8 m/s. Waves that are encountered by any kind of matter will
have a transmission of energy. This will cause the electrons into a
vibrational motion. When the electrons move they generate a field
causing a change in the transmitted wave. The electrons will move at a
resonant frequency to the vibration of the electrons. If the frequency
of the incident ray of light's electromagnetic wave does not have a
frequency matching this then the energy produced from this will create
a new electromagnetic wave. This wave will have a phase change from
the origninal wave. This change is a phase shift that slows down the
propagated wave. The photons that travel through the material still
travel at the speed of c. It has already been determined that photons
never travel at a speed other than that of c. They travel through the
empty space inbetween the atoms. They continue to travel until they
encounter another partice within the material. The whole process is
repeated and another new wave is produced. This cycle repeats as the
wave travels through the media encountering particle after
particle. The time delay that it takes for all the photons to travel
between the interatomic void is what causes the net speed of transfer
to be slower than the speed of c. The amount of time delay usually
depends on the optical density of the material. This describes how an
electromagnetic wave can move through a material.
There are two topics of optics that can be described. One is linear
optics and the other is nonlinear optics. In linear optics, the phase
shift is independent of the intensity. This has been demonstrated
through a beam so small that it was given an electric field much
smaller than the atomic field within the media. There was still a
refraction. If the intensity of the light beam can be considered
comparable to the atomic field then the distributions of the electrons
in the media will be modified because of the radiation. This will
cause an index of refraction based on the intensity of the incident
ray. This area is known as nonlinear optics. It is considered
nonlinear because the material will not respond in a linear matter
based on the amplitudes of the electric field. This means that the
index of refraction of a light beam is being controlled not by the
particular material but by the illumination of the incident ray of
light. This can open possibilities for manipulations of the
propogation of a beam of light with another beam of light.
The reason that the index of refraction will change because in
this material the light beam's frequency will be pushed through a
medium that will drive the molecules within it into a harmonic
motion. Typically when the electric force of the light beam is small
then the the vibration will be kept small and then frequency of the
light will remain constant. As long as the frequency is kept constnat
the medium will respond linearly. If a high power laser is used that
has a large amplitude E field, there will be a change in the frequency
of the reflection and refraction of the beam. An example where this
idea is applied is a red laser beam of 694.3nm is shone through a
transparent nonlinear crystal that is a second-harmonic generator and
the transmitted beam will be UV with a wavelength of 347.15nm. Some
crystals that can do this are potassium dihydrogen phosphate (KDP) and
ammonium dihydrogren phosphate (ADP).
This project however will focus on linear optics, where the index
of refraction is independent to the illumination of the light ray. The
ray that is used is a laser pointer.
Fermat's principle and Snell's law have been able to give accurate
predictions on the path of a ray of light because it is passing
through a boundary where it experiences a constant and clear change in
an index of refraction. When light passes through any kind of media it
will experience some kind of scattering that has been related to
Maxwell's Electromagnetic Theory. Through this the formula's for
Snell's law have been developed. It is also been noted that the
wavelength of the light will change while the frequency remains
constant. This is based on the principle that wavelength is equal to
the velocity divided by the frequency. This can also extend to the
idea that colors of lights are more closely related to their
frequencies because as they tranvserse medias their wavelengths may
differ but the frequencies will remain the same. The wavelengths that
are referred to in colors are the vaccuum wavelengths when the speed
of the transversing light is that of 3.00 e8 m/s.
When a beam of light is incident on an interface that has a greater
index of refraction than the transmitted medium, if the angle of
incidence is increased it is obsverved that the transmitted beam bends
more and more away from the normal toward the interface. The angle
where the light striking the interface is reflected back is known as
the critical ange. At the critical the transmitted angle will be 90
degrees. The light will never travel through the interface. Instead it
will be totally internally reflected. As long as the incident angle is
equal to or greater than the critical angle then 100% of the energy in
the incoming ebam is reflected back into the incident medium.
