Mechanical and Electromagnetic Vibrations and Waves

Chapter 8

Interference and Diffraction

If two beams of particles are intercepted on the same region of a screen, the energy, momentum and other physical quantities, which are received at each point, are the sums of the corresponding quantities for the beams if they are intercepted separately. This is not the case if two waves superpose in a region of space; the experiment shows that there is a redistribution of physical quantities. We say that the waves interfere. On the other hand, a free particle has rectilinear motion even if it passes near a body or through an aperture with which it does not interact. The experiment shows that a wave deviates from its straight-line propagation if it encounters an obstacle, or it passes through an aperture whose dimensions are comparable to the wavelength. This effect is known as diffraction. Interference and diffraction are two characteristic properties of waves; they are consequences of the superposition principle of waves and the quadratic dependence of the physical quantities on u.

In this chapter we study the interference and diffraction of mechanical and electromagnetic waves. In the case of vector waves, we assume that they are either longitudinal or transverse but polarized linearly in the same direction; this allows us to replace their vector sums by algebraic sums, just like in the case of scalar waves. We will not discuss the questions that are specific to optics, such as coherence, interference setups, effects of diffraction on ...