By C.E. Weatherburn

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**Additional resources for Advanced Vector Analysis with Application to Mathematical Physics **

**Example text**

Half-period zones. 4. 4a. Forward scattering Consider a spherical wave φ = (a0/r) exp [2ni(kr — vt)] from a source S incident on an infinite plane of atoms. SP is normal to the plane of atoms (Fig. 5). Let there be η atoms per unit area in the plane. Each will give rise to a scattered wave whose amplitude at a distance r' will be given by , φ = φ0af(Θ)/r , where φ0 is the amplitude of the incident wave and a f (θ) is the scattering power of the atom, which will depend on the nature of the incident radiation.

The magnitude of the extension was not One-dimensional Diffraction 31 discussed. It can be obtained most simply by considering first the diffraction by a single slit of a plane parallel beam of light, such as is produced by a laser. In this case the diffracted intensity will be significant only in or very close to the plane containing the direction of propagation of the beam and a line in the plane of the slit normal to its length. In this plane the intensity distribution will be that of Fig. 7.

The decrease in Rn with increasing η is due solely to the obliquity f a c t o r , / ( 0 ) , so we see that the area of a zone is proportional to its distance from P , these two factors in the amplitude exactly cancelling. If r' |> λ/2, the areas of successive zones will be very nearly the same, as may be shown directly. The radius of the outer boundary of the nth zone is therefore proportional to A diffracting screen constructed in such a way that it obstructs alternate zones between concentric rings whose radii increase as n* is known as a zone plate.