waves02

waves02 - 4 78 Int erferen ce and Diffra ct ion Sec. 9.6 4...

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4 78 Interference and Diffract ion Sec. 9.6 479 9.6 Diffract ion a nd fluygen,y' Principle Difference benceen interference and diffraction. In Sec. 9.5 we discussed the angular width of a diffra cti on-limited beam. w e gave a crude deriva- tion of th e diffr acti on patt ern produced wh en an infinite plan e wave stri kes an ap erture in an opaque screen (Fig. l Ob) or a mir ror (Fig. IOe) or is emitted by a plan e radi ator (Fig. I Od). In pr evious sec tions we discussed th e interfer en ce pattern produ ced by two point or line source s. Wh at is the di ffe rence betwee n an interferen ce pattern and a diffracti on patt ern ? None, really. For hist orical reasons, th e amplitude or intensity patt ern produced by superposing contributions from a finite number of discrete coherent sources is usually called an interf erence patt ern . Th e amplitude or intensity pattern produced by superpo sing the contributions from a "continuous" distri buti on of coherent sources is usually called a diffra ction patt ern. Th us one speaks of the interference patt ern from two narrow slits, or the diffraction patt ern from one wide slit, or the combined interference and diffraction patt ern from two wide slits. In Sec. 9.5 we assumed tha t the diffracti on-limited beam produ ced when a plane wave is incident on an apertur e in a screen (Fig. l Ob) is equivalent to that pro duced by a plane radia tor having the size of the aperture, with all parts of the radi ator oscillating in ph ase and with the same amplitude (Fig. 10d). In the present section we shall seek to justify thal assumed eq uivalence . In so doing, we shall find that th e equivalence is not exact; it is a useful approximation that greatly Simplifies the calculation of diffrac- tion patterns. It only works if the ape rt ure wid th is large compared with the wavelength. In th at case, it works very well for calculating the radia- tion emitted at not too large angles from the beam direction and thus for calculating th e int ensity and amplitude sufficiently far downstr eam from the aperture or equivalent radia tor. It is not of any use if you wish to know the fields inside the aperture itself. Th e calculation tech niqu e that makes use of this assumed eq uivalence is called H rlygens ' construction. We shall use it to calculate the diffraction patt ern produ ced when a plane wave (produced, for examp le, by a distant poin t source) strikes a hole in an opaque screen. How an opaque screen works. All elect roma gnetic radiati on has its ulti- mate origin in oscillating charged particles. The total elec tric (and mag- netic) field at any given point is a superposition of the waves produced by all the sources, i.e., all the oscillating charges. In the present problem, one of the sources is the distant point source that produces the plane wave in- cident on th e scree n. \ Ve shall call this th e source S. Behind the opaque scree n th e total wave amplitude is zero (by hypoth esis-that is wh at we mean by an opaque screen). This total wave is a superposition of the wave
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waves02 - 4 78 Int erferen ce and Diffra ct ion Sec. 9.6 4...

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