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Section 9.1: The Scattering of Classical Electromagnetic Waves



check, then click a link below to see the sum of the waves.

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A classical electromagnetic wave at an interface where there is a change of index of refraction is similar to, but not exactly the same as, a quantum-mechanical plane wave incident on a change in potential energy.

Change the index of refraction in the region on the right, Region II, and see what happens to the incident right-moving, transmitted right-moving, and reflected left-moving waves. Clicking in the check box enables you to see the sum of the incident and the reflected waves in Region I.  Note that the reflected wave travels in the opposite direction from the incident wave and is 180o out of phase with the incident wave at the interface.

The amplitude of the reflected wave becomes larger as n2 increases. When you add the incident wave to the phase-shifted reflected wave as the two amplitudes approach each other with increasing n2, the resultant wave in Region I will resemble a standing wave. This idea is important for the visualization of quantum-mechanical barrier problems. When an electromagnetic wave travels from a region of smaller n to a region of larger n, its wavelength and speed decrease. In addition, the amplitude of the transmitted electromagnetic wave becomes smaller as n increases.

Now change the index of refraction in the region on the left, Region I, and see what happens to the incident right-moving, transmitted right-moving, and reflected left-moving waves. The amplitude of the reflected wave becomes larger as n1 increases. When you add the incident wave to the reflected wave as n1 increases, the resultant wave in Region I will again resemble a standing wave. However, when an electromagnetic wave travels from a region of larger n to a region of smaller n, its wavelength and speed increase. In addition, the amplitude of the transmitted electromagnetic wave becomes larger as n increases.

The reflected wave's amplitude (and hence energy) is also related to the energy stored in the region (the dielectric).

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