Absolutely Small - Michael D. Fayer [37]
Figure 7.1 shows the geometry for light diffraction from a grating. The incoming light is at an angle α (Greek letter alpha) relative to the normal to the grating. The normal is the direction perpendicular to the surface of the grating. The grating is shown from the side. The surface of the grating, which looks like a flat mirror to the eye, has a dense set of parallel grooves in it. These grooves are called lines. The spacing between the lines is labeled d in Figure 7.2. The spacing is about the wavelength of light, approximately one ten millionth of a meter. The grooves are highly reflective. They are usually gold or silver. For incoming light that has a range of colors, the outgoing light will be separated by color such that each color goes in a unique direction. The separation into colors going in different directions is illustrated in Figure 7.1. The angle between the normal to the grating and a particular color is labeled β (Greek letter beta) in the figure. β is shown for the blue color. β is bigger for green and still bigger for red.
FIGURE 7.1. Geometry of light diffraction from a grating. The grating is composed of a reflective surface, usually silver or gold, with very fine parallel grooves in it. The grating is shown here from the side. The grooves run into the page. The grooves have a very uniform spacing, d; α is the angle of the incoming light. The outgoing angles β depend on the color. Therefore, the colors are separated by diffraction.
Diffraction of Light Shows Wave Character of Photons
The diffraction of light from a grating shows the wave nature of photon wave packets. To see that diffraction brings out the wave character of photons, we need to look at how diffraction works in terms of constructive and destructive interference of waves. Figure 7.2 shows incoming photon wave packets as a beam of light impinging on the diffraction grating. The light travels different distances before it strikes various parts of the grating. The light that reaches the upper left portion of the grating will travel a shorter distance than the light that hits the bottom right portion of the grating. The wave packet is composed of many colors, that is, many waves with wavelengths, λ. The different colors of light will come off of the grating in all directions. Here is the tricky part. The wave packets are more or less localized, but they are composed of different colors, each of which is a delocalized probability amplitude wave (see Figures 6.1, 6.2, 6.4, and 6.7). The more or less localized wave packet is formed by the interference of many different color waves (different λs, which correspond to different momenta, p). Consider one particular color, red, that comprises part of the wave packet. If the wave hits only one line in the grating, it would reflect off in many directions because of the shape of the groove. It would leave the single groove as a superposition state composed of probability amplitude waves propagating in many directions. In the interferometer (Figure 5.1), the incoming wave packet became a superposition state that had probability amplitude propagating in two directions. Here, after hitting a single line, the superposition would be heading in many directions.
The important feature of a grating is that the incoming wave hits many lines in the grating. For a particular color, red shown in Figure 7.2, there is a single direction in which the waves will add up constructively. In the figure, for the direction in which the red waves are propagating, all of the peaks and troughs of the waves add in phase even though they reflect from different places. (The wavelength has been exaggerated relative to the line spacing, d, to make it easy to see the alignment of the waves.) The in phase addition of many waves leaving the grating makes a very large outgoing wave. In all other directions, the red waves will add destructively because the peaks and null do not line up.
Diffraction from a grating causes the waves of a given wavelength (a particular color) to add constructively in one