(S-5) Waves and Photons
Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: "Waves and Photons," section #S-5: on disk Sun5wave.htm, on the web
Goals: The student will learn|
The lesson may be started with a discussion of waves.
What is a wave?|
The precise definition of a wave involves too much math (involving the so-called "the wave equation," which requires calculus), so instead let us take as a working definition of a wave "a disturbance spreading through space, usually carrying energy." It isn't completely accurate, but it covers the waves studied here.
What kinds of waves to you know--other than light and its relatives? (List on the board the types proposed by students, then fill in gaps)
Light belongs to the family of "Electromagnetic Waves," described more accurately later. Anyone knows other waves in this family? (List on the board, then fill gaps)
Unless raised by a student, the following is better skipped, to save time and potential confusion. Strictly speaking, any moving particles are also associated with so-called "matter waves." Such waves, describing the particle's "wave function" in quantum mechanics, are of a different kind, giving the probability of the particle being observed at various locations.)
(If someone mentions Alfvén waves or "whistlers", these are among known types of plasma waves, many of which are electromagnetic waves modified by the presence of plasma, for instance, in space around Earth.)
(If someone mentions "standing waves," these are waves of any kind confined between boundaries and therefore not traveling outside them. For instance, a wave on a guitar string, confined to the section between the bridge and the fret.)
What properties of a wave can we measure?
How do we find the relation between the wavelength, wave velocity and frequency? (Teacher starts the explanation)
The length v of the wave passing in one second through a given point in space contains many up-and-down swings, each of length λ. Their total number in that second is.... (a student may try complete on the board, or else, teacher continues)
(length of one wave)
So.... f = v/ λ
What difference does it make whether light is a wave or an array of "rays," of streams of "light particles"?
--In principle, a big difference:
(Teacher explains) For many years it was believed that light consisted of rays. The rays were bent by prisms or lenses, and the laws of such bending helped design telescopes and other instruments.
Then, however, scientists discovered interference--when two or more rays from the same source overlapped, they could reinforce or weaken each other--depending whether their crests overlapped (reinforced) or crest matched dip (=crest in opposite direction), in which case they were weakened.
The diffraction grating (discussed in the the preceding lesson) is an example. It was then realized that light was a wave, but with a very small wavelength. Beams of light are well defined on distance scales much larger than a wavelength, but they "fuzz out" when one tries to define their boundaries within a wavelength or less.
Before discussing why light was recognized as an electromagnetic wave, one should understand what "electromagnetic" means.
What is a magnetic field?
A magnetic field is the region in which magnetic forces can be observed--forces on an iron magnet or on an electric current.
What causes magnetic fields?
The magnetism of the Earth is believed to be caused by electric currents in its core. The magnetism of sunspots is also due to electric currents.
(Teacher explains) An electric field is similarly the region where electric forces can be observed. You comb your hair on a dry winter day and find the comb is electrified--it can attract little bits of paper, the way a magnet attracts pins. In that case, an electric field exists around the comb.
Similarly, friction among dry garments in a clothes dryer creates an electric field, which makes them cling to each other. In a laser printer or a xerox-type copier, a roller is electrified and finely powdered carbon sticks to it; later, under the influence of light, electric charge is removed preferentially, leaving it (and the carbon sticking to it) only where it contributes to the printed picture.
All these electric fields persist, because the comb, fabric, roller and surrounding air are all insulating materials, which do not allow electric charges to move freely. On the other hand, an electric field in a metal wire that conducts electricity (=allows charges to move) will move charges and will create an electric current. That is how home electricity works.
Now the big question: can electric fields ever drive electric currents in a vacuum or in an insulator--currents that creat magnetic fields? Usually--no. However... (students answer, teacher supplements)
The additional term was only significant if the electric field changed very rapidly. When the electric field stayed steady, the extra term was absent. Maxwell showed that such a wave had properties actually observed in light, and proposed that the added term was indeed necessary, and that light was an electromagnetic (EM) wave.
Light is usually produced by heat, or by glowing gases. If Maxwell was right, however, it should be possible to produce EM waves by purely electrical means. Can it be done?
What differences do you know between sound waves and electromagnetic (EM) waves?
[Do not raise the following point unless some student does. In electromagnetic waves, the disturbances--the electric and magnetic forces which mark the waves--are transverse to the direction in which the wave travels--see animated figure from section (S-5). The shaking is directed sideways--like a wave on a rope. Sound waves in air are longitudinal, with the oscillating pressure force along the direction in which the wave spreads. However, sound-like waves in solids--e.g. earthquake waves--may also be transverse.]
As an illustration of the 3rd difference above--how are windows on microwave ovens constructed--and why?
Most electromagnetic waves have a much higher frequency than sound waves--but not always. Ultrasound used in medicine and in cleaning small objects has a much higher frequency than the kind of sound we hear. And whistlers are electromagnetic waves in the same frequency range as regular sound, modified by the plasmas surrounding Earth and guided by the Earth's magnetic field lines--sometimes even bouncing back and forth along them, from one hemisphere to the other.
Whistlers can be picked up by long wire antennas. They were occasionally heard along the end of the 19th century, on long-distant telephone lines, sounding like long whistles dropping in pitch. In World War I (1914-8) they were heard on telephone lines employed by the armies in the field, and in 1919 the German scientist Heinrich Barkhausen proposed they were coming from outside Earth.
In 1953 Owen Storey showed that they were broadcast from lightning strokes. Lightning emits a wide range of radio frequencies, as first shown in 1895 by Aleksandr Stepanovich Popov in Russia--indeed, its crackling is easily picked up by ordinary radios during thunderstorms. Storey showed that whistlers often started from lightning in the opposite hemisphere, near the other end of the observer's magnetic field line, whose attached plasma guided them. Whistlers have since then provided unique information about the density of ions and electrons in space around Earth.
(end of optional section)
Light and other EM radiations spread like waves, all over space. However, the way they give up their energy is distinctly not wavelike. Can you describe it?
What quality of light determines the energy of its photons?
Photons of blue light have more energy then those of red, which in turn have more than those of infra-red, and all these are less energetic than photons of ultra-violet. The energies of X-rays are even larger, and gamma-ray photons have energies larger still.
What formula gives the connection between photon energy E and the light's frequency ν ?
You have an electric circuit triggered by an "electric eye," a tube empty of air with two metal contacts inside it. One is a plate of a suitable metal, with the property that, when light falls on it, it knocks out electrons. If the contacts are connected to a battery, the flow of such "photoelectrons ("photo" means, related to light) completes an electrical circuit, and if the circuit also contains an alarm, it will start ringing.
Question: You find that such a tube is triggered by blue light but not by red light. Can you guess the reason?
When developing film in a darkroom, no light is allowed, or else it would darken the exposed parts of the film. However, with old-type orthochromatic black-and-white film it was permissible to use a deep-red "safelight" in the darkroom. Why was this safe?
Why do glowing gases (e.g. neon lights) emit well-defined spectral colors?
(Optional historical note)
The first clue for energy levels in atoms came in 1885. By then, the wavelength of typical atomic emissions of light had been measured with great precision. Complicated elements emit hundreds and thousands of well-defined "spectral lines", but hydrogen, the simplest elements, seemed to have just 4 "lines" of specific colors. Johann Balmer, a high school math teacher in Basel, Switzerland, found that the wavelength of all four fit a formula
where n = 3,4,5.. and R is the experimentally obtained "Rydberg constant", later explained using quantum theory. (A translation of his original article exists on the web.)
The lowest of these "lines" (n=3) is the red "hydrogen alpha" line (Hα for short), responsible for the dominant red color of the visible chromosphere of the Sun. That is the layer of the solar atmosphere just above the photosphere from which most of visible sunlight originates (light emitted deeper down is just reabsorbed and re-emitted).
The chromosphere emits relatively little light, which is normally drowned out by the much greater brightness of the photosphere. It becomes visible during a total eclipse of the Sun. Then, after the Moon completely covers the photosphere, a reddish glow becomes visible around the Sun, in a relatively narrow ring; above it is the corona whose light is even fainter.
The chromosphere is important because it is the site of energy releases associated with sunspot magnetism--the so called solar flares. Solar flares are only rarely bright enough to show themselves against the background of the photosphere (one such rare event was the first flare to be observed, seen by Richard Carrington in 1859). All this changed with the introduction of sensitive filters which only transmitted the narrow Hα line and blocked everything else. Through such filters flare activity and many other solar phenomena can be clearly seen and photographed.
After Balmer announced his series, Lyman found in the ultra-violet a series of lines
of which the "Lyman α" line is particularly prominent in the glow of the Earth's outer atmosphere, photographed by astronauts from the Moon. Also, Paschen found a series of lines in the infra-red
All these are now understood to represent jumps of the hydrogen atom between two of its main energy levels R/n2 (n = 1,2,3...). This was one of the early indications that the frequency ν of light (proportional to 1/λ) gave a measure of an energy associated with it. Later "spectral lines" of other atoms were also found to represent jumps between a smaller number of levels, though their values did not fit simple mathematics, the way the levels of hydrogen did. The details were gradually worked out between about 1900 and 1930, as the "quantum theory" of atoms evolved.
(End of optional historical note)
Atoms in a gas emit photons individually, and the peaks of the waves they produce are randomly distributed. On the other hand, in a laser, between tuned mirrors (and for appropriate energy levels) the atoms can match their emissions, the way crickets or frogs at night sometimes coordinate their sounds into a single chorus. These ordered ("coherent") light waves can be modified to carry signals through "optical cables" of super-transparent glass fibers, much more efficiently than metal cables can do so
(end of optional section)
Why do pictures of the Sun taken in "soft" X-rays show mainly the corona?
Author and Curator: Dr. David P. Stern