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.
