Lecture26

Lecture26 - Physics 344 Foundations of 21st Century Physics...

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Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Fan Chen Office: PHYS 222 [email protected] Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: Chapters 2 and 3 in Six Ideas that Shaped Physics, Unit Q

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Maxwell’s Wave Model of Light We’ve developed enough of the differential form of Maxwell’s equations to analyze linearly polarized monochromatic plane waves starting from the fundamental principles of electromagnetism. We can superpose such waves to make all of the other predictions of the wave theory we need, so, they too are are based on fundamental principles. x y z 0 ˆ ( , , , ) cos x E x y z t E t y c ϖ φ = - + a 0 ˆ ( , , , ) cos E x B x y z t t z c c = - + a The fields of y -polarized monochromatic wave propagating in the x direction are There is also a z-polarized wave 0 ˆ ( , , , ) cos x E x y z t E t z c = - + a 0 ˆ ( , , , ) cos E x B x y z t t y c c = - - + a In both cases, is parallel to the wave vector . E B × a a ˆ k x c = a
Clearly, a plane wave propagating in the x direction can be linearly polarized with its electric field vectors oriented in any direction perpendicular to x (there is a coordinate system in which the E field vectors point in the ±y direction). As a first example of how superposition of monochromatic plane waves allows us to understand more complicated situations, we note that any of these waves can be represented as a superposition of the y - and z -polarized waves. ( 29 0 0 0 ˆ ˆ ( , , , ) cos cos ˆ ˆ cos x x E x y z t E t y E t z c c x E t y z c ϖ φ = - + + - + = - + + a For example, simple superposing the two in phase, yields electric and magnetic fields of a linearly polarized wave with its electric field oriented at 45 o relative the y axis. Here is the electric field, By shifting the relative amplitudes and phases of the y - and z -polarized waves we can represent any possible polarization of a monochromatic plane wave traveling in the x direction. We can choose two basic polarizations for a monochromatic plane wave with

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This note was uploaded on 12/09/2011 for the course PHYS 344 taught by Professor Garfinkel during the Fall '08 term at Purdue.

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Lecture26 - Physics 344 Foundations of 21st Century Physics...

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