An Introduction to the Theory of Diffraction by C. J. Ball and G. E. Bacon (Auth.)

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

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The two first-order spectra, St and S[, will be separated by a distance si = 2 / s i n θί9 where / i s the focal length of the lens. The amplitude due to these two sources at a point Ρ in the image plane a distance χ from Ο will be 2 a ^ o s {-Id) where A ί is the amplitude of each of the first-order spectra and D is the distance of the image plane from the focal plane. e. 0 or π (cos = + or — ), as can be seen from the sequence of amplitudephase diagrams in Fig. 19. SO exceeds π/2. 36 Theory of Diffraction d=2a (c) F I G .

The second term on the right, 2 varying as y , is identical with the corresponding phase difference for the Two-dimensional 49 Diffraction 2 2 forward scattered and reflected waves if sin 0 = sin 6", and is never very different. The wave scattered in the direction 0 " will therefore be comparable in intensity with the other scattered waves, any difference arising mainly through the different value of/(Θ). F I G . 7. Geometry of scattering by a plane of a t o m s in a crystal. A t o m s are situated only o n the lines shown.

The diffraction pattern of a single slit produced with a plane parallel beam therefore approximates to a distribution of intensity within a very narrow ribbon. To consider the diffraction pattern produced by a single slit when illuminated with the arrangement shown in Fig. 14, we suppose that each infinitesimal element of area in the collimator slit gives rise to a strictly parallel beam, and hence to a diffraction pattern of the type produced with a laser, as discussed above. If we divide the collimator slit into strips of infinitesimal width parallel to the slit, then the elements of area within each strip will give rise to diffraction patterns that are displaced relative to one another in a direction at right angles to their direction of extension, as in Fig.

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