By C. J. Ball and G. E. Bacon (Auth.)
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Extra info for An Introduction to the Theory of Diffraction
Two-dimensional Diffraction 53 In Fig. 10 a plane parallel beam of light is incident normally on a screen in which there is an aperture : we wish to determine the intensity in some arbitrary direction specified by the angles θ and φ. A general method of doing this is as follows: take Cartesian axes x, y and ζ with the x-axis parallel to the incident beam direction and the j - a x i s in the plane defined by the x-axis and the direction in which we wish to determine the intensity. The phase difference between wavelets from Incident plane wave F I G .
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. This result can be obtained from eq. 3) by putting I0 = 1/N , One-dimensional Diffraction 29 to give a zero order maximum of unit intensity, and approximating 2 2 sin y by y .
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. 4d. Validity of Fresnel zone treatment The assumption that the resultant of the scattered waves from the whole plane will be half that from the first Fresnel zone, with a phase shift of π/2 relative to the wave from the centre of the zone, will be valid only if the amplitude-phase diagram converges to the centre of the initial circle. Convergence, however, is very slow in the cases considered.
An Introduction to the Theory of Diffraction by C. J. Ball and G. E. Bacon (Auth.)