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By C. J. Ball and G. E. Bacon (Auth.)

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Extra info for An Introduction to the Theory of Diffraction

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This is illustrated in Fig. 8. If, by chance, the boundary of the atom plane happens to lie within only a very few zones (in an extreme case, within one zone), then there will be variations in intensity around P. In practice this would not be observed, even with measuring instruments of unlimited resolution, since the angle between the directions of maximum intensity would be very much less than the angle subtended by the source, unless the atom plane were very small indeed. Another way of looking at the problem is that in the radiation from an extended source phase coherence is not maintained over long distances, because neither are the wavefronts strictly planar, nor is their form constant with time.

In practice this would be done n o t graphically b u t from a table of the Fresnel integrals, as in the following example. 5b. Example We will calculate the intensity of the light in a plane at a distance χ = 0-1 m m behind the edge of an opaque screen when it is illuminated 5 with a beam of light of wavelength 5 χ 1 0 ~ cm, as in Fig. 8. F o r this case s = (2klxfy = (2x2xl0 ,710 -2fy 3 = 2 χ 10 j; (y in cm) = 0-2>> (y in μπι). 1. Each line of the table show the stages in the calculation of the intensity at one value of y.

8. =o j3=0 r 2π π π/2 3π 4π 5π 3 π /2 F I G . 12. Principal m a x i m a in Fraunhofer intensity distribution for a diffraction grating of ten lines with d = 3a. The angular distribution of intensity for a grating with ten lines for which d = 3a is shown in Fig. 12. Note that the width of each principal maximum is the same. For a grating with a large number of lines, for which the intensity of the subsidiary maxima falls to a small fraction of the intensity of the principal maxima quite close to the latter, the intensity distribution around each of the principal maxima is the same as in the diffraction pattern of a single slit of width equal to the total width of the 2 grating.

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