Light

=The Basics=

Electromagnetic radiation*
toc Hans Christen Orsted - demonstrated electric field also have magnetic fields. Compass needle twitched when current passed through a wire. Since nothing moves without a force, there much be a magnetic force on the compass. This discovery led to the possibility of creating motors. Michael Faraday - discovered //electromagnetic induction//; moving magnets creates electricity. This discovery ed to creating dynamos or electric generators and transformer. J.C. Maxwell - Unified electromagnestism and light with 4 laws. Used a wave as a solution to these equations that traveled at the speed of light. Henric Hertz - measured electromagnetic field and determined wavelengths and velocities of radio waves. William Roetgen - discovered X-rays Albert Einstein - explained the photoelectric effect; 4 discoveries
 * Historic Pioneers**
 * 1) Force exists between two charges (Coulomb's Law)
 * 2) Magnetic poles in pairs; no magnetic monopoles
 * 3) Changes in electric field make magnetic field (Orsted's discovery)
 * 4) Changes in magnetic field make elextric field (Faraday's discovery)
 * 1) Special Relativity
 * 2) Equivalence of mass and energy
 * 3) Brownian Motion
 * 4) Described photoelectric effect

[\Details]
 * Dispersion
 * Light Spectrum
 * Prisms, Gratings
 * Energy/Light relation
 * Particle-Wave Duality
 * Netwon
 * Huygens

Electromagnetic Spectrum
== Radio waves - Microwaves - 2.45 GHz used to cook food, can by focused in beams for communication; point to point direction (cell phones); radar used to detect objects Infrared -emittted by every hot object as heat Visible light - where we see colors Ultraviolet - able to damage tissue; UVA, UVB (far UV) and UVC (extreme UV): used to study surface of solids and absorbed by ozone X-rays - highest waves produced by conventional means; can ionize atoms. gamma rays - only produced in the nuclei when protons accelerate (unlike oscillating EM waves); used in medical science

=Historic Observations= The Ultraviolet Catastrophe [\Predicted the power radiated from a blackbody increases to inifinite frequencies, but it actually decreases to 0] [\Observed standing waves of certain frequency can only exist at certain invervals] [\Plank solved the problem] [\r.http://en.wikipedia.org/wiki/Ultraviolet_catastrophe] [\http://www.youtube.com/watch?v=cW4vmr3hb2o&feature=related]

The Photoelectric Effect
Around the time of J.J. Thomas, some observations were made that were not understood. At the time, light was known to exhibit wave-like properties, which was an uncontested argument after the famous double slit experiment by Thomas Young in 1801. The following experiments were conducted:
 * Experiment 1: If light of a certain frequency is shown on a metal, electrons can be ejected. If the light frequency is less than the threshold frequency, no electrons are liberated. If the frequency is greater than the threshold frequency, electrons are liberated. This was curious because there was no known relation between the frequency of light and energy.
 * Experiment 2: when higher frequencies were used, only a constant number of electrons were released. This was also curious as it was expected that the electron number would scale with frequency.
 * Experiment 3: Higher intensity did not affect the kinetic energy
 * Experiment 4: There was a linear relationship between the number of electrons and the intensity.

It was Einstein who plotted the kinetic energy vs. time for several metals. He notices that all of the metals were linearly related and had the same slope with a value equivalent to //Plank's constant//. He established that hv is indeed an energy term. This suggests the for a given wavelength, energy is packaged in units of h. This gave the idea that light was series of particles called //photons//. hv_0 (the intercept of the linear relationships) is the minimum energy required to eject an electron, a.k.a., the //work function//.

Particle-Wave Duality
The number of electrons do not add up in energy to eject a photon. The number of electrons do scale with the number of electrons ejected. The transfer of momentum, proposed by Einstein and confirmed by Compton (x-rays lost momentum after hitting electrons, "Compton scattering"), gave stronger evidence that light behaved as particles. p=h/v. deBroglie suggested that all matter behaved like waves. That is the wavelength of any matter can be calculated if both e mass and velocity is known;

math {\lambda}=\frac{h}{mv} math

The wavelength of electrons is comparable to the size of atoms. Thus moving electrons can impact atoms, which is observed through diffraction experiments.

Schr**ö**dinger equation
The **Schr****ö****dinger equation** describes particles as a wave-like function. When the an operation is performed on the wavefunction (specifically the Hamiltonian operator, //H//), a binding energy (E) and the wavefunction result. The standing wave equation (time-independent) is written:

math \hat H \psi = E \psi math

The general wave equation assumes a single hydrogen atom. Schrodinger associates energy and orbitals with electrons. Solving for the binding energy indicates that the allowable energy states of a bound electron is quantized into discrete states, which is inversely proportional to the square of principle quantum number (n) by the negative Rydberg constant (-R_d). Two facts are extracted from solving the binding energy of the Schrödinger equation:

1.) The principle quantum number is extracted. 2.) The ground state of an atom is most stable when it is closely bound to an atom.

Solving the wave-function generates two additional quantum numbers. Three quantum numbers are required to describe an wave-function in three dimensional space, i.e. an orbital.

Designates the shell. || n = 1,2,3...infinity || \psi math || Describes orbital shapes via angular and rotational information. Designates the subshell. || l = 0, 1, 2, 3 ... n-1 || \psi math || Tells behavior of electron in a magnetic field. It is a component of the angular momentum. Completely describes the orbital. || -l ... 0... l ||
 * ~ Quantum Number ||~ Name ||~ Where derived from S.E. ||~ What is tells us ||~ Limits ||
 * = n ||= Principle ||= E || Shows the quantization of energy states of a bound electron to a nuclues.
 * = l ||= Angular ||= math
 * = m_l ||= Magnetic ||= math

The fourth quantum number completely describes the intrinsic properties of the electron. While there is no classical description, the 4th quantum number can be viewed as an electron spinning on its axis clockwise (spin up) or counter-clockwise (spin down). The electron spin behavior can be observed in NMR spectroscopy in the form of doublets as two protons interact.
 * ~ l = ||~ oribital ||~ origin of names ||
 * 0 || s || sharp line ||
 * 1 || p || principle line ||
 * 2 || d || diffuse line ||
 * 3 || f || fundamental line ||

In summary, an orbital is completely decribed by three quantum numbers. An electron within an orbital is described by four quantum numbers.

\psi_{nlm_l} math ||= math \psi_{nlm_l m_s} math ||
 * ~ Description for an ||
 * ~ Orbital ||~ Electron ||
 * = math

=EM Properties=

Binding Energy
Solving the //binding energy// (E) in Schr**ö**dinger equation unveils a number of key principles in spectroscopic analysis. First, binding energy is the energy required to excited a ground state electron to a higher bound state. Excessive exciting can liberate an electron to an unbound state a.k.a. //free electron//. This process can lead to several phenomena including ionization, photo emission or absorption of energy.

Ionization Energy
The ionization energy is the difference between the free electron energy state and the ground state. The ionization energy of a ground state atom is the negative of the Rydberg constant. This is equivalent to the amount of energy that must be put into a system to eject an electron. This differs from electron affinity, which is the likelihood of a electron to be added to an atom, i.e. Cl has a high electron affinity for making Cl- (ΔE = -349 kJ/mol).

Bound atoms hold on the electrons more loosely than independent atoms.
 * Note: The energy required to liberate an electron from...
 * A solid material = work function
 * A free atom = ionization energy

= =

=Interactions of Light with Matter=

Emission
In the 1700s, science burned matter and split the the emitting light with a prism. The resulting spectra was not continuous but had gaps with sharp spectral peaks (this is in contrast to heated solid bodies that radiate continuous spectra at different wavelengths depending on temperature). The spectra indicated that gases of certain substances had specific spectral signatures. Spectral lines emitted by a hydrogen atom are divided into sets of series where the difference between some initial energy state and a specific final state (terminated at n) is related to a specific frequency (or specific color in the visible range). Bohr's orbital model where each electron is associated with allowed orbits of certain energy could accurately predict the positions of transmission spectral lines. Therefore, the spectral lines suggest the energy released from electrons at certain orbital positions (quantum number, n). math \frac{1}{\lambda} = \frac {-R}{h} \left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right) math
 * ~ n ||~ series ||~ light ||
 * 1 || Lyman || UV ||
 * 2 || Balmer || visible ||
 * 3 || Paschen || near IR ||
 * 4 || Brackett || IR ||

The Rydberg equation is modified formula of an empirical formula determined by Balmer and used for hydrogen. Once an elecromagnetic wave is emitted by a shaking charge, there are three options for the life of the wave:
 * 1) Transmission: EM waves transfer through transparent medium
 * 2) Absorption: EM waves are absorbed and translated into another form of energy, i.e. heat
 * 3) Light Scattering: light bounces in some other direction.
 * 4) Diffuse scattering (Lambertian): light scatters in various directions
 * 5) Reflection: special scattering from a smooth metallic surface
 * 6) Diffraction: interference with planar features in a mirror i.e. fringe effects

Transmission
[\Beer's Law]

Absorption*

 * Poynting Vector

What happens to molecules when you shine light?
 * Light || Wavelength || Effect ||
 * Radio ||  ||   ||
 * Microwave ||  || Molecules rotate violently which produces heat. ||
 * Infrared ||  || Molecules vibrate ||
 * Visible ||  ||   ||
 * Ultraviolet ||  || Electrons are raised to higher energy states ||
 * X-ray ||  || Electrons are removed from shells ||
 * Gamma ||  ||   ||

Light Scattering*

 * Fraunhoefer theory
 * Mie theory
 * Rayleigh theory
 * Applications: Laser light scattering
 * Why the sky is blue, clouds are white, setting sun is red. Water droplets are larger than 1 um, therefore, light scatters unpreferentially. Light scattering is 10x stronger for blue light than red. Thermal fluctuations lead to density fluctuations in the sky which act as scatters. When the sun sets, red light appears because higher engery light (blue, green) has scattered out of the incident beam.
 * Diffuse Scattering
 * Reflection
 * Diffraction

Colors*
The light transmitted from an object is complementary to the light which is adsorbed. In 1800, William Herschel tried to measure the temperatures of colors in the spectrum. He discovered that the hottest temperature existed for a colorless part of the spectrum. This he named //infrared// (below red). John Ritter heard of these discoveries of light beyond the visible spectrum and designed an experiment to investigate beyond the violet end of the spectrum. He tested silver chloride in each color of the spectrum. Silver chloride turns darkest closest to the blue end than in red. He discovered the darkening of silver chloride occurred beyond the violet end in a region he called Chemical Rays, later to be renamed //ultraviolet//.

Polarization*

 * Unpolarized Light
 * Total Internal Reflection
 * Malus Law
 * Brewster Angle: the special angle at which light is completely polarized.

Quantum Electrodynamics
Quantum Electrodynamics (QED) is a science founded on mathematical rigor to describe light propagating through space and time and its interaction with elemental particles. Feynman's classic lectures simplifies the fundamentals of this complex field as he describes the basics of electrodynamics, which requires an appreciation for the following insights:
 * quantum mechanics
 * phasors and probability amplitudes
 * space-time continuum
 * feynman diagrams
 * the electric field as the force applied by photons

Three laws of QED

 * 1) Electrons travel from point to point
 * 2) Photons travel from point to point
 * 3) Electrons emit and absorb photons.

Relativity
According to Einstein, light appears to slow down as the observer approaches the speed of light called time //dilation//. Equations with light includes the //Lorentz Factor// where t = sqrt(1-(v/c)^2). This phenomena is only observed in cosmoslogical particles and particle accelerators. The greater the relative velocity, the greather the mass of the object, which is inversely propotional to the Lorentz Factor. This phenomena of an object's resistance to reach the speed of light by increasing mass is actually observed in particle accelerators, where objects reaching higher velocities approach an infinite mass.

=References=