Ch0222

# Ch0222 - Chapter 22 Huygenss Principle and 2-Slit Interference 22 Huygenss Principle and 2-Slit Interference Consider a professor standing in front

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Chapter 22 Huygens’s Principle and 2-Slit Interference 192 22 Huygens’s Principle and 2-Slit Interference Consider a professor standing in front of the room holding one end of a piece of rope that extends, except for sag, horizontally away from her in what we’ll call the forward direction. She asks, “What causes sinusoidal waves?” You say, “Something oscillating.” “Correct,” she replies. Then she starts moving her hand up and down and, right before your eyes, waves appear in the rope. For purposes of discussion, we will consider the waves only before any of them reach the other end, so we are dealing with traveling waves, not standing waves. “What, specifically, is causing these waves,” she asks, while pointing, with her other hand, at the waves in the rope. You answer that it is her hand oscillating up and down that is causing the waves and again you are right. Now suppose you focus your attention on a point in the rope, call it point P, somewhat forward of her hand. Like all points in the rope where the wave is, that point is simply oscillating up and down. At points forward of point P, the rope is behaving just as if the professor were holding the rope at point P and moving her hand up and down the same way that point P is actually moving up and down. Someone studying only those parts of the rope forward of point P would have no way of knowing that the professor is actually holding onto the rope at a point further back and that point P is simply undergoing its part of the wave motion caused by the professors hand at the end of the rope. For points forward of point P, things are the same as if point P were the source of the waves. For predicting wave behavior forward of point P, we can treat point P, an oscillating bit of the rope, as if it were the source of the waves. This idea that you can treat one point in a wave medium as if it were the source of the waves forward of it, is called Huygens’s Principle. Here, we have discussed it in terms of a one dimensional medium, the rope. When we go to more than one dimension, we can do the same kind of thing, but we have more than one point in the wave medium contributing to the wave behavior at forward points. In the case of light, that which is oscillating are the electric field and the magnetic field. For smooth regular light waves traveling in a forward direction, if we know enough about the electric and magnetic fields at all points on some imaginary surface through which all the light is passing, we can determine what the light waves will be like forward of that surface by treating all points on the surface as if they were point sources of electromagnetic waves. For any point forward of the surface, we just have to (vectorially) add up all the contributions to the electric and magnetic fields at that one point, from all the “point sources” on the imaginary surface. In this chapter and the next, we use this Huygens’s Principle idea in a few simple cases (e.g. when, except for two points on the kind of surface just mentioned, all the light is blocked at the surface

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## This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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Ch0222 - Chapter 22 Huygenss Principle and 2-Slit Interference 22 Huygenss Principle and 2-Slit Interference Consider a professor standing in front

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