The propagation of light

The propagation of light - Maxwell's equations at speed c...

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The propagation of light. We can conclude from Maxwell's equations that light is in fact an oscillation of the electric and magnetic fields that propagates through free space with velocity c = 1/ . Moreover, the electric and magnetic fields are always mutually orthogonal and always in-phase. Since electric and magnetic field have an associated energy, their propagation causes the transport of energy and momentum. For this reason it is possible to calculate the energy density (energy per unit volume) of an electric or magnetic field. In SI units these turn out to be: u E = u B = Since μ 0 = 1/ ε 0 c 2 and | in SI units, then u B = u E . This should not be a surprising result--it simply says the energy is divided equally between the electric and magnetic fields. The total energy u is just u = u E + u B = 2 u E = ε 0 E 2 = . Now the wave is propagating in a direction perpendicular to both the electric and magnetic fields (this can be proved from
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Unformatted text preview: Maxwell's equations) at speed c . Therefore, the power incident on an area perpendicular to the direction of travel will have an amount of energy flow through it every second of uc . This can be seen from the dimensions of energy/volume × distance/second = energy per area per second. This is the incident power, S . Thus, S = uc = = c 2 ε EB . We can express this more usefully as a vector , perpendicular to and and normal to the surface across which the power per unit area is being calculated. This gives: This is called the Poynting vector. Figure %: Direction of propagation of an electromagnetic wave. Thus light is a form of electromagnetic radiation, just like radiowaves, microwaves, infrared rays, X-rays, gamma rays and cosmic rays. It has frequencies in the range 3.84×10 14 Hz to 7.69×10 14 Hz, which corresponds to wavelengths of 780 to 390 nanometers....
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This note was uploaded on 02/09/2012 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.

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The propagation of light - Maxwell's equations at speed c...

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