Electromagnetic radiation constructive interference

FIGURE 1.19 In this illustration, the peaks of the waves of electromagnetic radiation are represented by orange lines. When radiation coming from the left (the vertical lines) passes through a pair of closely spaced slits, circ ular waves are generated at each slit. These waves interfere with each other. Where they interfere constructively (as indicated by the positions of the dotted lines), a bright line is seen on the screen behind the slits where the interference is destructive, the screen is dark. 

When two or more waves pass through the same region of space, the phenomenon of interference is observed as an increase or a decrease in the total amplitude of the wave (recall Fig. 1.20). Constructive interference, an increase in the total amplitude of the wave, occurs when the peaks of one wave coincide with the peaks of another wave. If the waves are electromagnetic radiation, the increased amplitude corresponds to an increased intensity of the radiation. Destructive interference, a decrease in the total amplitude of the waves, occurs when the peaks of one wave coincide with the troughs of the other wave it results in a reduction in intensity. 

Diffraction is described by either Bragg or von Laue equations. The Bragg equation relates as a condition for constructive interference the wavelength of the electromagnetic radiation k to the interplanar distance a and the observation angle 0... 

Experiments with light in the nineteenth century and earlier were consistent with the view that light is a wave phenomenon. One of the more obvious experimental verifications of this is provided by the interference pattern produced when light from a point source is allowed to pass through a pair of slits and then to fall on a screen. The resulting interference patterns are understandable only in terms of the constructive and destructive interference of waves. The differential equations of Maxwell, which provided the connection between electromagnetic radiation and the basic laws of physics, also indicated that light is a wave. 

The intensity of a particular X-ray diffraction also depends partly on phase effects. Recall that electromagnetic radiation can constructively interfere or destructively interfere, as shown in Figure 21.16. For some crystals in which diffraction from a plane of atoms is expected to occur, it turns out that diffraction from an adjacent plane contributes X rays of the exact opposite phase The result is complete destructive interference, and the intensity of this expected diffraction is zero. This is the reason that odd values of the sum h + Ic + are absent for body-centered... 

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