The Nature of Light - Part 2 (From Young to Maxwell)

In the wave theory of light we assume light is an infinite continues monochromatic plane wave.

The constant A is the amplitude of the waveand T is the period, andis the wavelength. The wave is traveling along x-axis. This suggested model for light could explain the Young’s experiment until they realized that wave is a state of material and it propagates by the means of matter.

However we know that light travels in free space where there is no matter to let the wave travel. This problem was answered with Maxwell’s equation in electromagnetic wave where the wave was riding on electric and magnetic fields.

Maxwell’s equations in free space:

The first equation says if electric field changes by time, it causes the magnetic field changes in different way, which is the curl of magnetic field at that point. The second equation says that if magnetic field changes with time it similarly causes the curl of electric field at that point, which means we once more have a changing electric field but this new electric field is a bit distant from the original changing electric field. Maxwell says that the changing electric field travels with the speed of light.

If we assume that the electromagnetic wave is one dimensional field such as then the field becomes a function of x and t resulting in:

In addition we now can predict the plane waveform for the electric and magnetic fields:

The Maxwell’s electromagnetic wave including and . (Goldin,120)

The energy is associated with this electromagnetic wave is the average energy of the sum of electric and magnetic fields:

For the complete solution of the electromagnetic wave we need to conclude the boundary conditions and all harmonic waves.

If we choose the length L somehow that E(x,t) = E(x+L,t) applies and then:

The Nature of Light - Part 1 (From Newton to Young)

Mohsen Mirtalebi

ECE491

Prof. Maher Rizkalla

Final Report

Photoelectric Effect in Charge Couple Devices

2009 Update: I wrote this paper several years ago as the final report to a single credit summer course for a college project. I do not intend to change its structure as it reflects a stance of my life.

Abstract

This paper is to bring a mathematical model of light from Maxwell and Einstein’s points of view and the effect of photon on MOSFET devices. The article will start an introductory concept of light through Newton law and then it proceeds to show the evolution of our understanding about light in electromagnetic form as well as it as an entity in quantum mechanics. Then this paper will emphasize on the mathematical model of light in post electromagnetic form explained by photon model. Finally, it will adopt the photon form of light to explain the photoelectric energy conversion in charge-coupled devices. It has been always fascinating for me to write and talk about light.

From Newton to Einstein

Isaac Newton recognized light as a beam of particles. His theory about light could very well answer why light travels in a straight line. In addition, his theory could comply with rules in geometric optics and the properties of mirror, lenses, and prism. In the Newtonian fashion, light is shown as a straight line.

The glass prism spreads white light out into a spectrum. (Baierlein, 16)

But Newton’s theory failed when it came to explain diffraction and interference of light. Thomas Young set up an experiment that Newton’s theory could not answer the mechanism of the his experiment. He allowed sunlight to pass through a pinhole in the sheet S1 and then pass through two pinholes in sheet S2 and observing the result on the sheet S3. The result was bunch of dark and light stripes.

Young’s experiment’s set up. (Goldin, 91)

Young’s experiment’s real results. (Goldin, 90)