## Light

By the mid 1800s, it was already well understood that light behaves as a wave: it can be polarized and can produce interference patterns. The nature of light waves was a mystery, however. How did light travel through apparently “empty” space (e.g. between the sun and the earth), where there is no air or other known substance to act as a medium?  If a wave is an oscillating disturbance, what exactly is being oscillated or disturbed when light waves travel through space?

The mystery was finally solved by James Clerk Maxwell, who presented his theory of light to the Royal Society in 1864.The full text of Maxwell’s lecture, published in 1865, is available here. Maxwell’s third and fourth equations imply that changes in the magnetic field cause changes in the electric field, and vice versa. He realized that this mutual relationship would allow transverse waves to propagate through the electric and magnetic fields, even where no charged particles are present. Moreover, the speed at which these waves must propagate is determined by two quantities (namely, permittivity and permeability) that appear in his equations.See Appendix B. [link coming soon] The values of those quantities could be measured, so Maxwell was able to calculate how fast the waves should travel through empty space: approximately three hundred million meters per second. That is the speed of light, which had already been measured in numerous experiments by other physicists. Maxwell concluded that light and electromagnetic waves are the same thing! Light consists of electromagnetic waves, or electromagnetic radiation—waves oscillating in the electric and magnetic fields.

Measuring the speed of light
The most accurate measurement of the speed of light, prior to the publication of Maxwell’s result, was achieved by French physicist Leon Foucault in 1862. In Foucault’s experiment, a rotating mirror was placed 20 miles away from a stationary mirror. A beam of light was reflected from the rotating mirror to the stationary mirror and back again. In the extremely brief time that it took the beam of light to make that 40-mile round trip, the rotating mirror would turn only slightly, but it was enough to deflect the returning light at a noticeable angle compared to its original trajectory. By measuring the angle of deflection and the rate of the mirror’s rotation, Foucault was able to determine the speed of light to within 0.3% of the actual value, which was measured more precisely by experiments in the 20th century. Eventually, these experiments achieved such a high degree of precision that physicists decided to redefine the length of the meter in terms of the speed of light, rather than vice versa! The meter is now defined as 1/299792458th of the distance light travels in a second. For this reason, the speed of light is exactly 299,792,458 meters per second.

### The electromagnetic spectrum

Our eyes perceive different wavelengths of light as different colors. We see long wavelengths of light as the color red, for example, and the shortest wavelength we can see is the color violet. This relation between wavelength and color had already been discovered in the early 1800s, before anyone knew what kind of waves light consisted of. As early as 1802, Thomas Young proposed that colors correspond to different wavelengths of light. He also correctly hypothesized that color vision depends on three different types of light receptors in the human eye, each tuned to a certain range of wavelengths. His lecture, “On the theory of light and colours,’ is available here. This theory of color vision was further developed in 1850 by Hermann von Helmholtz. However, when Maxwell recognized that light is electromagnetic radiation, he also noticed that his equations predicted something unexpected: there should be other wavelengths of light beyond the colors our eyes can see! There should be light with wavelengths longer than red, and light with wavelengths shorter than violet. Could these invisible forms of light be detected? In 1886, two decades after Maxwell had published his theory of light, German physicist Heinrich Hertz began a series of experiments to test Maxwell’s predictions. Hertz successfully devised instruments to detect much longer wavelengths of light than our eyes can see. The invisible, long-wavelength electromagnetic waves he discovered are known today as radio waves.

Other invisible forms of light were discovered soon afterwards, with wavelengths ranging from thousands of kilometers long to extremely short wavelengths, even shorter than the diameter of a single atom. Visible light, with wavelengths between 700 nanometers (red) and 400 nanometers (violet), is just a tiny fraction of the full electromagnetic spectrum. In order from longest wavelength to shortest, the electromagnetic spectrum includes radio waves, microwaves, infrared light, visible light, ultraviolet light, x-rays, and gamma rays. These diverse forms of electromagnetic radiation are, in essence, just different colors of light. Most of these “colors” are invisible to human eyes, of course, though some animals can see infrared and ultraviolet light. There are far more colors of light than the colors we see!

All forms of electromagnetic radiation consist of waves oscillating in the electric and magnetic fields, and all of these electromagnetic waves travel at the speed predicted by Maxwell’s equations—that is, the speed of light. Since they all travel at the same speed, wavelength and frequency are correlated: the shorter the wavelength, the higher the frequency of the oscillations. For example, blue light has a shorter wavelength—and thus higher frequency—than red light. Moreover, high-frequency waves carry more energy than low-frequency waves, since it takes more energy to oscillate the electric and magnetic fields more rapidly. (The concept of energy will be explained and discussed in the next chapter.) Radio waves have the longest wavelength, and thus also have the lowest frequency and lowest energy. Gamma rays have the shortest wavelength, and therefore the highest frequency and highest energy. Visible light lies in the middle of the spectrum and ranges from red (lower frequency and energy, but not as low as infrared) to violet light (higher frequency and energy, but not as high as ultraviolet).

### Sources of electromagnetic radiation

Electromagnetic waves are produced whenever a charged object is accelerated. For example, if you rub a plastic comb through your hair to give it an electrical charge, then accelerate the comb by waving it back and forth, radio waves will be produced. (These extremely low-frequency waves will be too weak to detect with an ordinary radio receiver, however.) The acceleration of the charged comb disturbs the electric and magnetic fields, creating a wave that oscillates through those fields like ripples on a pond.

Similarly, atoms emit electromagnetic waves whenever they are accelerated, because atoms contain charged particles (electrons and protons). Any change in the velocity of an atom produces an electromagnetic wave, and ordinary material objects like apples and chairs contain trillions of atoms that are always jiggling around and bumping into each other. For this reason, material objects constantly emit electromagnetic radiation. Light produced in this way is called thermal radiation, and its color depends on the temperature of the object. An object’s temperature is related to the motions of its molecules and atoms, as we’ll see in the next chapter. The hotter the object, the faster its atoms jiggle around. So, hot objects emit higher frequencies of thermal radiation than cold objects. Objects at room temperature emit mostly infrared light, which we cannot see. If you heat up an object enough, though, it emits visible light as well, beginning with the color red—the lowest-frequency color of light that our eyes can detect. When heated even more, it emits all colors of visible light at once, and our eyes interpret that mixture of waves as the color white. This is why a piece of metal begins to glow deep red, then bright orange, and eventually white when heated with a furnace or torch.

As we’ll see in chapter 4, light is also produced when an electron falls from a high-energy state to a low-energy state inside an atom. Often, this light is in the visible part of the spectrum. Something similar happens when protons and neutrons shift states inside the nucleus of an atom, as we’ll see in chapter 5; but changes to the nucleus of an atom release extremely energetic forms of light—usually gamma rays. Other processes can produce light as well. Understanding the nature of light and how it is produced will be important in chapter 8, when we examine the leading theories of contemporary astronomy and cosmology. Astronomers can gather an astonishing amount of information about distant stars, galaxies, and other celestial objects simply by studying the specific colors of light that these objects emit.

### Transmission, absorption, and scattering

When an electromagnetic wave hits matter, one of three processes occurs:

• The wave may be scattered (i.e., absorbed and instantly reemitted in a different direction). Depending on the type of material and texture of its surface, this may happen in one of two ways:
• Diffuse scattering occurs when reemitted light waves go in random directions.
• Reflection occurs when light waves are reemitted from a flat surface at an angle equivalent to the angle at which they came in. (The angle of incidence equals the angle of reflection.)
• The wave may be transmitted through the matter. However, the speed at which electromagnetic waves travel through matter is slower than the speed of light through empty space. How much slower depends on the type of material and also on the wavelength of the light:
• Short wavelength (high frequency) waves slow down more; long wavelength (low frequency) waves slow down less.
• In denser materials, light tends to slow down more. The degree to which light slows down in any given material is determined by that material’s index of refraction—the ratio of the speed of light in a vacuum to the speed of light in that material.
• The wave may be absorbed by the matter. The wave stops, and the energy of the matter increases (e.g. by rising in temperature) by an amount equivalent to the energy of the wave. A wave may also be partly absorbed. That is, some of its energy may be absorbed by the matter, while the remaining energy is either scattered or transmitted in the form of a lower-energy wave (a wave with lower frequency and longer wavelength).

Refraction (bending of light) occurs when an electromagnetic wave passes through one material into another at an angle—for example, when it goes from air into glass or water. As light passes from a faster material into a slower one, it bends in the direction toward the slower material. To understand why this happens, an analogy may be helpful. Imagine a simple toy that consists of two wheels side-by-side, connected with an axle. You roll this toy across a smooth floor, and it hits a patch of carpet at an angle. The carpet slows the toy. Because the toy hits the carpet at an angle, one of the wheels slows down before the other, and the toy turns in that direction. That’s essentially what happens with light (except that unlike the toy, light speeds up again after it comes out of a slower material).

Shorter wavelengths are affected by refraction more strongly than longer wavelengths. For example, violet light bends more sharply than red light as it passes through a glass prism. To continue the simple toy analogy, shorter wavelengths are like smaller wheels that are affected more dramatically when they hit the carpet; longer wavelengths are like bigger wheels that only slow down a little when they roll onto carpet.

The effects of diffuse scattering also depend on wavelength. For example, blue and violet colors of light tend to scatter more as they pass through the earth’s atmosphere, while red and yellow colors scatter less. That’s why the sky appears blue! Light from the sun is white: a mixture of all the colors. But the blue and violet waves tend to scatter through the atmosphere, reaching our eyes from all directions so that the sky appears to have a blueish hue. This also explains why the sun looks yellow (rather than white), and why the sun appears redder near the horizon. The more atmosphere the sunlight has to pass through to reach us, the more the blue and violet colors are scattered away, making the sun appear redder than it really is.