Absolutely Small - Michael D. Fayer [15]
Waves do not have to be right on top of each other and going in the same direction to interfere. They just have to overlap in some region of space, and interference can occur in that region. When Davies Symphony Hall in San Francisco was opened in 1980, it had acoustic problems. While the problems were very complicated, it is easy to see how they developed. Imagine that you are sitting in the audience pretty far back from the orchestra. When a 440 Hz A is played, the acoustic wave comes directly at you but it also bounces off of the walls on either side of you. If there is a reflection from the wall to your right and a reflection from the wall to you left so that the reflected acoustic waves (sound waves) from each wall comes to your row of seats at, for example, a 30° angle, an interference pattern will be produced along your row of seats. There will be places where reflected waves constructively interfere and make the sound louder and places where the waves destructively interfere and make the sound softer. The spacing between a peak and a null of the interference pattern is 2.4 ft (see below for the spacing formula). So depending on your seat, the 440 Hz A will be louder or softer. Of course, there are many frequency acoustic waves coming at you from many directions. The combined interference effects distorted the sound that should have been coming straight at you from the orchestra. The problem in Davies Hall was fixed in 1992 by the installation of 88 carefully designed panels hanging from the ceiling along the two side walls. No two panels are identical. They are filled with sand and weigh as much as 8500 pounds. These panels prevented the reflections from the walls from going into the audience.
Light can also undergo interference phenomena. The classical view of optical interference patterns can reproduce experimental results, as we are about to see. However, as discussed in Chapters 4 and 5, ultimately the classical description fails when other experiments are considered. The correct description will introduce the quantum mechanical superposition principle and bring us back to Schrödinger’s Cats.
Figure 3.4 shows a diagram of an interferometer used by Michelson (Albert Abraham Michelson, 1853-1931) in his studies of the nature of light waves. Michelson won the Nobel Prize in Physics in 1907 “for his optical precision instruments and the spectroscopic and metrological investigations carried out with their aid.” Michelson and Morley, who was a coworker of Michelson, used an interferometer to attempt to determine the nature of the medium in which light waves propagated. Water waves propagate in water. Sound waves propagate in air. The Michelson-Morley experiment showed that light waves do not have an underlying medium, which had been called the aether. Light can propagate in a vacuum. There is no aether that pervades space. Light waves traveling to us from the stars are not traveling in a medium the way ocean waves and sound waves travel in water and air, respectively. This was an important step in recognizing that light waves are not waves in the same sense as sound waves. Here we only want to understand the classical description of what is observed with an interferometer.
FIGURE 3.4. The incoming light wave hits a 50% reflecting mirror. Half of the light goes through the mirror and half reflects from it. The light in each leg of the interferometer reflects from the end mirrors. Part of each beam crosses in the overlap region at a small angle. To the right of the circled overlap region is a blowup of what is seen along the x direction when two beams cross. An interference pattern is formed in which the intensity varies along x from a maximum value to zero periodically.
In Figure 3.4, a beam of light, taken to be a light wave, enters the apparatus from the left. The light hits a partially reflecting “beam-splitting” mirror that reflects 50% of the light intensity and transmits 50% of the light intensity. In the wave description of light, there is no problem having part of the wave go one way and part the