Monday, October 5, 2009

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:


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