Chapter 2 (Particle Properties of Waves) Review: Wave Properties of Waves

Chapter 2 Particle Properties of Waves Overview During his investigations of the photoelectric effect ca , Hertz made some observations about light which could not be explained by the wave properties of electromagnetic radiation. You’ll hear more about the photoelectric effect in the next lecture. Heinrich Hertz was a German physicist who showed that radio waves (not known as such back then, of course) and light are both examples of the electromagnetic waves described by Maxwell’s equations.

The Compton effect, explained by Compton in 1923 while he was at Washington University in St. Louis, involves the change in wavelength of x-rays when they are scattered.* *Nobel Prize, The Compton effect cannot be explained by the wave properties of electromagnetic radiation. We will skip this section of the text. We have some unsolved “issues” with electromagnetic radation. But first, let’s review what you already know.

2.1 Electromagnetic WavesElectromagnetic Waves This section is a review of material you should already know. Consider a wave described by The phase of this wave is Also

If  is constant with time (i.e., d  /dt=0), then we are moving with the wave, and The phase velocity, v p, is given by Note that k=2  /, so if  is a nonlinear function of k, then the phase velocity depends on. Imagine yourself riding on any point on this wave. The point you are riding moves to the right. The velocity it moves at is v p.

The spatial coordinate of any point of constant phase travels in the +x direction when  /k is positive, and in the -x direction when  /k is negative. The wave is moving from left to right so  /k must be positive. In other words, waves travel to the right when  /k is positive, and to the left when  /k is negative. Thus, the signs of  and k tell the direction of motion of the phase of a wave.

In Physics 201, you may have derived a classical expression for the energy per unit time carried by a wave. The result is The power depends on  2 (or f 2 ) if the amplitude A is constant, or on A 2 if  is constant. As we will see in the next section, the experimental results of the photoelectric effect are in disagreement with this equation

Superposition -- a characteristic of all waves. When waves of the same nature travel past some point at the same time, the amplitude at that point is the sum of the amplitudes of all the waves The amplitude of the electric field at a point is found by adding the instantaneous amplitudes, including the phase, of all electric waves at that point. If A = a + jb is an amplitude, then A * = a - jb and Remember that power (or intensity) is proportional to amplitude squared.

Superposition is a result of the linear relations between electric field and polarization and between magnetic field and magnetization. The magnitude of a wave is found by multiplying the amplitude by its complex conjugate. The intensity of the superposed waves is proportional to the square of the amplitude of the resulting sum of waves.

Interference -- a result of the superposition of waves. Constructive Interference: If the waves are in phase, they reinforce to produce a wave of greater amplitude. Destructive Interference: If the waves are out of phase, they reinforce to produce a wave of reduced amplitude.

Web pages on interference: actions/index.html

Young’s Double Slit Experiment (1801) This experiment demonstrates the wave nature of light. Consider a single light source, and two slits. Each slit acts as a secondary source of light (this is a result of diffraction; the light waves bend around corners at the slits). Light waves from secondary slits interfere to produce alternating maxima and minima in the intensity. Reference and “toy:” interference/doubleslit/index.html. interference/doubleslit/index.html

How does this work? Light waves from the two slits arriving at the detection screen in phase will interfere constructively and light waves arriving out of phase will interfere destructively. In phase— constructive. Out of phase— destructive.

 is the path length difference. Interference is constructive when  =, 2, 3... Interference is destructive when  = /2, 3 /2, 5 /2… For path lengths in between, the interference is only partial. In fact, the familiar n = a sin  applies here, where 2  is the angle between the two rays at the screen. 

More “toys:” two-slit2.html Useful reference page:

So What? Interference and diffraction are exclusively wave-like properties. So is refraction (also a property of light and waves). We conclude that light is clearly a wave. Maxwell studied electromagnetic waves. Maxwell showed what kind of wave light is. Maxwell, 1864, suggested that accelerated electric charges generate electromagnetic waves. Faraday then showed that a changing magnetic field can induce a current. Maxwell proposed that a changing electric field has an associated magnetic field. This was confirmed only after his unfortunate death.

Maxwell showed that electromagnetic waves propagated with the speed This is exactly the speed of light, and Maxwell concluded light consists of electromagnetic waves. Note that light waves are only a small part of the electromagnetic spectrum.

Electromagnetic waves propagate at the speed of light in a vacuum, but slower in materials, which makes the index of refraction greater than unity (n = c/v). Hertz provided experimental confirmation of electromagnetic waves in The experimental confirmation was found in the photoelectric effect. When asked by a student what these experiments meant, Hertz supposedly said “It’s of no use whatsoever. It just proves Maxwell was right.” When the student then asked “so, what next?” Hertz supposedly replied “nothing, I guess.”* *Hertz was brilliant but excessively modest. Every day you benefit from dozens of applications based on his work. I’m not sure I believe this “story” but you can search for sources on the web if you are curious. Unfortunately, Hertz died at age 37 of blood poisoning.