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Unformatted text preview: 1 PHYS809 Class 33 Notes Refraction and reflection of electromagnetic plane waves Suppose two linear media are separated by a plane. A monochromatic wave incident on the plane in medium 1 will, in general, result in a reflected wave in medium 1 and a transmitted wave in medium 2. Each wave will have the same frequency but the wavelength will be different in the two media. Consider the situation shown below We have chosen the z-axis normal to the plane interface and the x-axis so that the wave vectors all lie in the xz plane. That the wave vectors all lie in the same plane is a consequence of the need to satisfy the boundary conditions at all points on the interface. Thus i r t = = k x k x k x on z = 0 . In other words, the projections of the wave vectors on to the interface are all parallel. Since by construction the y component of the incident wave vector is zero, the y components of the reflected and transmitted wave vectors are also zero. The x components of the wave vectors are all equal so that, using the notation of the figure, we get sin sin sin . i r t k i k r k t = = (33.1) Since k i and k r are in the same medium, we have k i = k r , which shows that the reflected angle equals the incident angle. Since the waves all have the same frequency, 1 1 2 2 1 1 . i t k k = = (33.2) In terms of the angle of incidence and the angle of refraction, this gives Snells law i 1 1 2 2 sin ....
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- Fall '11