3.1: Light

Defining Light

In everyday language, radiation is often used to describe certain kinds of energetic subatomic particles released by radioactive materials in our environment, or radioactivity. This is not what we mean when we use the word radiation in astronomy. Instead, radiation is a general term for waves that radiate outward from a source. The visible light and other radiation we receive from the stars and planets is generated by processes at the atomic level, by changes in the way the parts of an atom interact and move. To understand how light is generated, we must explore how atoms work. One of the key ideas explored in this chapter is that visible light is not unique, it is merely the most familiar example of a much larger family of radiation that can carry information to us.

Electromagnetism

We will look at the structure of the atom in more detail later, but we begin by noting that the typical atom consists of several types of particles, a number of which have not only mass but an additional property called electric charge. In the nucleus (central part) of every atom are protons, which are positively charged; outside the nucleus are electrons, which have a negative charge.

In the nineteenth century, many physicists turned to the study of electricity and magnetism, which are intimately connected with the production of light, including the physicist James Clerk Maxwell. Inspired by a number of ingenious experiments that showed an intimate relationship between electricity and magnetism, Maxwell developed a theory that describes both electricity and magnetism with only a small number of simple equations. It is this theory that gives us important insights into the nature and behavior of light. Maxwell unified the rules governing electricity and magnetism into a coherent theory.

Maxwell's theory deals with these electric charges and their effects, especially when they are moving. In the vicinity of an electron charge, another charge feels a force of attraction or repulsion: opposite charges attract; like charges repel. When charges are not in motion, we observe only this electric attraction or repulsion. If charges are in motion, however (as they are inside every atom and in a wire carrying a current), then we measure another force called magnetism.

Magnetism was well known for much of recorded human history, but its cause was not understood until the nineteenth century. Experiments with electric charges demonstrated that magnetism was the result of moving charged particles. Sometimes, the motion is clear, as in the coils of heavy wire that make an industrial electromagnet. Other times, it is more subtle, as in the kind of magnet you buy in a hardware store, in which many of the electrons inside the atoms are spinning in roughly the same direction; it is the alignment of their motion that causes the material to become magnetic.

Physicists use the word field to describe the action of forces that one object exerts on other distant objects. For example, we say the Sun produces a gravitational field that controls Earth's orbit, even though the Sun and Earth do not come directly into contact. Using this terminology, we can say that stationary electric charges produce electric fields, and moving electric charges also produce magnetic fields.

Electromagnetic Waves

Actually, the relationship between electric and magnetic phenomena is even more profound. Experiments showed that changing magnetic fields could produce electric currents (and thus changing electric fields), and changing electric currents could in turn produce changing magnetic fields. So once begun, electric and magnetic field changes could continue to trigger each other.

Maxwell analyzed what would happen if electric charges were oscillating (moving constantly back and forth) and found that the resulting pattern of electric and magnetic fields would spread out and travel rapidly through space. Something similar happens when a raindrop strikes the surface of water or a frog jumps into a pond. The disturbance moves outward and creates a pattern we call a wave in the water. You might, at first, think that there must be very few situations in nature where electric charges oscillate, but this is not at all the case. As we shall see, atoms and molecules (which consist of charged particles) oscillate back and forth all the time. The resulting electromagnetic disturbances are among the most common phenomena in the universe.

Maxwell was able to calculate the speed at which an electromagnetic disturbance moves through space; he found that it is equal to the speed of light, which had been measured experimentally. On that basis, he speculated that light was one form of a family of possible electromagnetic disturbances called electromagnetic radiation, a conclusion that was again confirmed in laboratory experiments. When light enters a human eye, its changing electric and magnetic fields stimulate nerve endings, which then transmit the information contained in these changing fields to the brain. The science of astronomy is primarily about analyzing radiation from distant objects to understand what they are and how they work.

The Wave-Like Characteristics of Light

The changing electric and magnetic fields in light are similar to the waves that can be set up in a quiet pool of water. In both cases, the disturbance travels rapidly outward from the point of origin and can use its energy to disturb other things farther away. For example, in water, the expanding ripples moving away from our frog could disturb the peace of a dragonfly resting on a leaf in the same pool. In the case of electromagnetic waves, the radiation generated by a transmitting antenna full of charged particles and moving electrons at your local radio station can, sometime later, disturb a group of electrons in your car radio antenna and bring you the news and weather while you are driving to class or work in the morning.

The waves generated by charged particles differ from water waves in some profound ways, however. Water waves require water to travel in. The sound waves we hear, to give another example, are pressure disturbances that require air to travel though. But electromagnetic waves do not require water or air: the fields generate each other and so can move through a vacuum (such as outer space). This was such a disturbing idea to nineteenth-century scientists that they actually made up a substance to fill all of space—one for which there was not a single shred of evidence—just so light waves could have something to travel through: they called it the aether. Today, we know that there is no aether and that electromagnetic waves have no trouble at all moving through empty space.

The other difference is that all electromagnetic waves move at the same speed in empty space (the speed of light—approximately 300,000 kilometers per second, or 300,000,000 meters per second, which can also be written as \(3 \times 10^8 \text{ m/s}\)), which turns out to be the fastest possible speed in the universe. No matter where electromagnetic waves are generated from and no matter what other properties they have, when they are moving (and not interacting with matter), they move at the speed of light. Yet you know from everyday experience that there are different kinds of light. For example, we perceive that light waves differ from one another in a property we call color. Let's see how we can denote the differences among the whole broad family of electromagnetic waves.

The nice thing about a wave is that it is a repeating phenomenon. Whether it is the up-and-down motion of a water wave or the changing electric and magnetic fields in a wave of light, the pattern of disturbance repeats in a cyclical way. Thus, any wave motion can be characterized by a series of crests and troughs, as depicted in Figure \(\PageIndex{1}\). Moving from one crest through a trough to the next crest completes one cycle. The horizontal length covered by one cycle is called the wavelength. Ocean waves provide an analogy: the wavelength is the distance that separates successive wave crests.

Figure \(\PageIndex{1}\) : Characterizing Waves. Electromagnetic radiation has wave-like characteristics: the wavelength (λ) is the distance between crests, and the frequency (f) is the number of cycles per second. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{1}\).

For visible light, our eyes perceive different wavelengths as different colors: red, for example, is the longest visible wavelength, and violet is the shortest. The main colors of visible light from longest to shortest wavelength can be remembered using the mnemonic ROY G BIV—for Red, Orange, Yellow, Green, Blue, Indigo, and Violet. Other invisible forms of electromagnetic radiation have different wavelengths, as we will see in the next section.

We can also characterize different waves by their frequency, the number of wave cycles that pass by per second. If you count 10 crests moving by each second, for example, then the frequency is 10 cycles per second (cps). In honor of Heinrich Hertz, the physicist who—inspired by Maxwell's work—discovered radio waves, a cps is also called a hertz (Hz). Take a look at your radio, for example, and you will see the channel assigned to each radio station is characterized by its frequency, usually in units of KHz (kilohertz, or thousands of hertz) or MHz (megahertz, or millions of hertz).

Wavelength (λ) and frequency (f) are related because all electromagnetic waves travel at the same speed. To see how this works, imagine a parade in which everyone is forced by prevailing traffic conditions to move at exactly the same speed. You stand on a corner and watch the waves of marchers come by. First you see row after row of miniature ponies. Because they are not very large and, therefore, have a shorter wavelength, a good number of the ponies can move past you each minute; we can say they have a high frequency. Next, however, come several rows of circus elephants. The elephants are large and marching at the same speed as the ponies, so far fewer of them can march past you per minute: Because they have a wider spacing (longer wavelength), they represent a lower frequency.

The formula for this relationship can be expressed as follows: for any wave motion, the speed at which a wave moves equals the frequency times the wavelength. Waves with longer wavelengths have lower frequencies. Mathematically, we can express this as

\[c = \lambda f \nonumber\]

where the Greek letter for “l”—lambda, λ—is used to denote wavelength and c is the scientific symbol for the speed of light. Solving for the wavelength, this is expressed as:

\[\lambda = \frac{c}{f} \nonumber\]

Light as a Photon

The electromagnetic wave model of light was one of the great triumphs of nineteenth-century science. In 1887, when Heinrich Hertz actually made invisible electromagnetic waves (what today are called radio waves) on one side of a room and detected them on the other side, it ushered in a new era that led to the modern age of telecommunications. His experiment ultimately led to the technologies of television, cell phones, and today's wireless networks around the globe.

However, by the beginning of the twentieth century, more sophisticated experiments had revealed that light behaves in certain ways that cannot be explained by the wave model. Reluctantly, physicists had to accept that sometimes light behaves more like a “particle”—or at least a self-contained packet of energy—than a wave. We call such a packet of electromagnetic energy a photon.

The fact that light behaves like a wave in certain experiments and like a particle in others was a very surprising and unlikely idea. After all, our common sense says that waves and particles are opposite concepts. On one hand, a wave is a repeating disturbance that, by its very nature, is not in only one place, but spreads out. A particle, on the other hand, is something that can be in only one place at any given time. Strange as it sounds, though, countless experiments now confirm that electromagnetic radiation can sometimes behave like a wave and at other times like a particle.

Then, again, perhaps we shouldn't be surprised that something that always travels at the “speed limit” of the universe and doesn't need a medium to travel through might not obey our everyday common sense ideas. The confusion that this wave-particle duality of light caused in physics was eventually resolved by the introduction of a more complicated theory of waves and particles, now called quantum mechanics. This is one of the most interesting fields of modern science, but it is mostly beyond the scope of our book. If you are interested in it, see some of the suggested resources at the end of this chapter.

In any case, you should now be prepared when scientists (or the authors of this book) sometimes discuss electromagnetic radiation as if it consisted of waves and at other times refer to it as a stream of photons. A photon (being a packet of energy) carries a specific amount of energy. We can use the idea of energy to connect the photon and wave models. How much energy a photon has depends on its frequency when you think about it as a wave. A low-energy radio wave has a low frequency as a wave, while a high-energy X-ray at your dentist's office is a high-frequency wave. Among the colors of visible light, violet-light photons have the highest energy and red-light photons have the lowest.

Test whether the connection between photons and waves is clear to you. In the above example, which photon would have the longer wavelength as a wave: the radio wave or the X-ray? If you answered the radio wave, you are correct. Radio waves have a lower frequency, so the wave cycles are longer (they are elephants, not miniature ponies).

Propagation of Light

Let's think for a moment about how light from a lightbulb moves through space. As waves expand, they travel away from the bulb, not just toward your eyes but in all directions. They must therefore cover an ever-widening space. Yet the total amount of light available can't change once the light has left the bulb. This means that, as the same expanding shell of light covers a larger and larger area, there must be less and less of it in any given place. Light gets weaker and weaker as it gets farther from its source.

The increase in the area that the light must cover is proportional to the square of the distance that the light has traveled, as demonstrated in Figure \(\PageIndex{2}\). If we stand twice as far from the source, our eyes will intercept two-squared (2 × 2), or four times less light. If we stand 10 times farther from the source, we get 10-squared, or 100 times less light. You can see how this weakening means trouble for sources of light at astronomical distances. One of the nearest stars, Alpha Centauri A, emits about the same total energy as the Sun. But it is about 270,000 times farther away, and so it appears about 73 billion times fainter. No wonder the stars, which close-up would look more or less like the Sun, look like faint pinpoints of light from far away.

Figure \(\PageIndex{2}\) : Brightness and Distance. As light spreads out from its source, the same amount of energy covers an increasingly larger area, so the energy received decreases as the square of the distance from the source. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{2}\).

This idea—that the apparent brightness of a source (how bright it looks to us) gets weaker with distance in the way we have described—is known as the inverse square law for light propagation. In this respect, the propagation of light is similar to the effects of gravity. Remember that the force of gravity between two attracting masses is also inversely proportional to the square of their separation.

Luminosity

Perhaps the most important characteristic of a star is its luminosity—the total amount of energy at all wavelengths that it emits per second. Earlier, we saw that the Sun puts out a tremendous amount of energy every second. And there are stars far more luminous than the Sun out there. To make the comparison among stars easy, astronomers express the luminosity of other stars in terms of the Sun's luminosity. For example, the luminosity of Sirius is about 25 times that of the Sun. We use the symbol L_Sun to denote the Sun's luminosity; hence, that of Sirius can be written as 25 L_Sun. In a later chapter, we will see that if we can measure how much energy a star emits and we also know its mass, then we can calculate how long it can continue to shine before it exhausts its nuclear energy and begins to die.

The Electromagnetic Spectrum

Objects in the universe send out an enormous range of electromagnetic radiation. Scientists call this range the electromagnetic spectrum, which they have divided into a number of categories. The spectrum is shown in Figure \(\PageIndex{1}\), with some information about the waves in each part or band. The Electromagnetic Spectrum, or EMS, is the range of frequencies of electromagnetic radiation. From shortest wavelengths to longest, the groups in the electromagnetic spectrum are gamma-rays, X-rays, ultraviolet, optical, infrared, microwaves, and radio waves. This is also the order from highest to lowest energy.

Figure \(\PageIndex{1}\) : The Electromagnetic Spectrum. The electromagnetic spectrum spans from gamma rays, the shortest wavelength and highest energy, to radio waves, the longest wavelength and lowest energy. (CC BY-SA 3.0; Jonathan S Urie via Wikimedia Commons) Accessible description of Figure \(\PageIndex{1}\).

Grouping by Wavelength

Astronomers use all parts of the electromagnetic spectrum because each type has its advantages and disadvantages. Some wavelength ranges can only be observed from space, because they are absorbed or scattered by Earth's atmosphere. The main region that is easily observed on the surface of Earth is visible light, and even that light is disturbed by turbulence in the atmosphere. Figure \(\PageIndex{2}\) includes examples of the extra information found at different wavelengths of electromagnetic radiation. Image (a) is a visible light image, with straight lines connecting the bright stars to form the outline of the constellation. Image (b) is the same area as Image (a) in X-rays, revealing many bright objects that are absent in Image (a). Image (c) is an infrared image, that includes only a few stars, and reveals delicate wisps of clouds which get quite bright and dense in the vicinity of the Orion nebula, near Orion's belt and sword. Images like (b) and (c) are sometimes called false color-images because they use visible colors to represent wavelengths that are not detectable by the human eye.

Figure \(\PageIndex{2}\) : Orion in Different Wavelengths. The same region of sky appears different depending on wavelength: (a) visible light traces the familiar stars of the constellation, (b) X-rays reveal point-like sources not seen in visible light, and (c) infrared light highlights glowing dust clouds near the Orion Nebula. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{2}\).

Electromagnetic radiation with the shortest wavelengths, no longer than 0.01 nanometer, is categorized as gamma rays (1 nanometer = 10^–9 meters). The name gamma comes from the third letter of the Greek alphabet: gamma rays were the third kind of radiation discovered coming from radioactive atoms when physicists first investigated their behavior. Because gamma rays carry a lot of energy, they can be dangerous for living tissues. Gamma radiation is generated deep in the interior of stars, as well as by some of the most violent phenomena in the universe, such as the deaths of stars and the merging of stellar corpses. Gamma rays coming to Earth are absorbed by our atmosphere before they reach the ground (which is a good thing for our health); thus, they can only be studied using instruments in space.

Electromagnetic radiation with wavelengths between 0.01 nanometer and 20 nanometers is referred to as X-rays. Being more energetic than visible light, X-rays are able to penetrate soft tissues but not bones, and so allow us to make images of the shadows of the bones inside us. While X-rays can penetrate a short length of human flesh, they are stopped by the large numbers of atoms in Earth's atmosphere with which they interact. Thus, X-ray astronomy (like gamma-ray astronomy) could not develop until we invented ways of sending instruments above our atmosphere. Figure \(\PageIndex{3}\) is an image of the entire sky seen in x-rays, with different colors (red, yellow, and blue) representing different x-ray energies. Red outlines the glow from a hot local bubble of gas all around us, blown by one or more exploding stars in our cosmic vicinity. Yellow and blue show more distant sources of X-rays, such as remnants of other exploded stars or the active center of our galaxy.

Figure \(\PageIndex{3}\) : X-Ray Sky. This false-color, all-sky X-ray map is tilted so the Milky Way's disk runs across the center; red, yellow, and blue mark X-rays of increasing energy, from a nearby hot gas bubble to more distant sources near the galaxy's center. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{3}\).

Radiation intermediate between X-rays and visible light is ultraviolet (meaning higher energy than violet). Outside the world of science, ultraviolet light is sometimes called “black light” because our eyes cannot see it. Ultraviolet radiation is mostly blocked by the ozone layer of Earth's atmosphere, but a small fraction of ultraviolet rays from our Sun do penetrate to cause sunburn or, in extreme cases of overexposure, skin cancer in human beings. Ultraviolet astronomy is also best done from space.

Electromagnetic radiation with wavelengths between roughly 400 and 700 nm is called visible light because these are the waves that human vision can perceive. This is also the band of the electromagnetic spectrum that most readily reaches Earth's surface. These two observations are not coincidental: human eyes evolved to see the kinds of waves that arrive from the Sun most effectively. Visible light penetrates Earth's atmosphere effectively, except when it is temporarily blocked by clouds.

Between visible light and radio waves are the wavelengths of infrared or heat radiation. Astronomer William Herschel first discovered infrared in 1800 while trying to measure the temperatures of different colors of sunlight spread out into a spectrum. He noticed that when he accidentally positioned his thermometer beyond the reddest color, it still registered heating due to some invisible energy coming from the Sun. This was the first hint about the existence of the other (invisible) bands of the electromagnetic spectrum, although it would take many decades for our full understanding to develop.

A heat lamp radiates mostly infrared radiation, and the nerve endings in our skin are sensitive to this band of the electromagnetic spectrum. Infrared waves are absorbed by water and carbon dioxide molecules, which are more concentrated low in Earth's atmosphere. For this reason, infrared astronomy is best done from high mountaintops, high-flying airplanes, and spacecraft.

After infrared comes the familiar microwave, used in short-wave communication and microwave ovens. Wavelengths vary from 1 millimeter to 1 meter and are absorbed by water vapor, which makes them effective in heating foods. The “micro-” prefix refers to the fact that microwaves are small in comparison to radio waves, the next on the spectrum. You may remember that tea—which is full of water—heats up quickly in your microwave oven, while a ceramic cup—from which water has been removed by baking—stays cool in comparison.

All electromagnetic waves longer than microwaves are called radio waves, but this is so broad a category that we generally divide it into several subsections. Among the most familiar of these are radar waves, which are used in radar guns by traffic officers to determine vehicle speeds, and AM radio waves, which were the first to be developed for broadcasting. The wavelengths of these different categories range from over a meter to hundreds of meters, and other radio radiation can have wavelengths as long as several kilometers.

With such a wide range of wavelengths, not all radio waves interact with Earth's atmosphere in the same way. FM and TV waves are not absorbed and can travel easily through our atmosphere. AM radio waves are absorbed or reflected by a layer in Earth's atmosphere called the ionosphere (the ionosphere is a layer of charged particles at the top of our atmosphere, produced by interactions with sunlight and charged particles that are ejected from the Sun).

Table \(\PageIndex{1}\) summarizes the bands of the electromagnetic spectrum and indicates the temperatures and typical astronomical objects that emit each kind of electromagnetic radiation. While at first, some of the types of radiation listed in the table may seem unfamiliar, you will get to know them better as your astronomy course continues. You can return to this table as you learn more about the types of objects astronomers study. Note that the shortest wavelength radiation detects the highest temperature objects. For example, the solar corona is detected in X-rays and has a temperature of 10⁶–10⁸ K. Meanwhile, long wavelength radio waves detect objects cooler than 10,000 K such as cold gas in space.

Table \(\PageIndex{1}\): Types of Electromagnetic Radiation

Type of Radiation	Wavelength Range (nm)	Radiated by Objects at This Temperature	Typical Sources
Gamma rays	Less than 0.01	More than 10^8 K	Produced in nuclear reactions; require very high-energy processes
X-rays	0.01–20	10^6–10^8 K	Gas in clusters of galaxies, supernova remnants, solar corona
Ultraviolet	20–400	10^4–10^6 K	Supernova remnants, very hot stars
Visible	400–700	10^3–10^4 K	Stars
Infrared	10^3–10^6	10–10^3 K	Cool clouds of dust and gas, planets, moons
Microwave	10^6–10^9	Less than 10 K	Active galaxies, pulsars, cosmic background radiation
Radio	More than 10^9	Less than 10 K	Supernova remnants, pulsars, cold gas

Further Exploration

• Watch Neil deGrasse Tyson and Chuck Nice explain The Electromagnetic Spectrum on Star Talk.

Examples and Exercises

Example: The Wave Equation

The equation for the relationship between the speed and other characteristics of a wave can be derived from our basic understanding of motion. The average speed of anything that is moving is:

\[\text{average speed} = \frac{\text{distance}}{\text{time}} \nonumber\]

So, for example, a car on the highway traveling at a speed of 100 km/h covers 100 km during the time of 1 h. For an electromagnetic wave to travel the distance of one of its wavelengths, λ, at the speed of light, c, we have \(c = \frac{\lambda}{t}\). The frequency of a wave is the number of cycles per second. If a wave has a frequency of a million cycles per second, then the time for each cycle to go by is a millionth of a second. So, in general, \(t = \frac{1}{f}\). Substituting into our wave equation, we get \(c = \lambda \times f\). Now let's use this to calculate an example. What is the wavelength of visible light that has a frequency of \(5.66 \times 10^{14} \text{ Hz}\)?

Solution

Solving the wave equation for wavelength, we find:

\[\lambda = \frac{c}{f} \nonumber\]

Substituting our values gives:

\[\lambda = \frac{3.00 \times 10^{8} \text{ m/s}}{5.66 \times 10^{14} \text{ Hz}} = 5.30 \times 10^{-7} \text{ m} \nonumber\]

This answer can also be written as 530 nm, which is in the yellow-green part of the visible spectrum (nm stands for nanometers, where the term “nano” means “billionths”).

Exercise: The Wave Equation

“Tidal waves,” or tsunamis, are waves caused by earthquakes that travel rapidly through the ocean. If a tsunami travels at the speed of 600 km/h and approaches a shore at a rate of one wave crest every 15 min (4 waves/h), what would be the distance between those wave crests at sea?

Answer

\(\lambda = \frac{600 \text{ km/h}}{4 \text{ waves/h}} = 150 \text{ km}\)

Example: Brightness with Distance

The intensity of a 120-W lightbulb observed from a distance 2 m away is 2.4 W/m². What would be the intensity if this distance was doubled?

Solution

If we move twice as far away, then the answer will change according to the inverse square of the distance, so the new intensity will be \(\left(\frac{1}{2}\right)^2 = \frac{1}{4}\) of the original intensity, or 0.6 W/m².

Exercise: Brightness with Distance

How many times brighter or fainter would a star appear if it were moved to:

1. twice its present distance?
2. ten times its present distance?
3. half its present distance?

Answer

 

a. \(\left(\frac{1}{2}\right)^2 = \frac{1}{4}\); b. \(\left(\frac{1}{10}\right)^2 = \frac{1}{100}\); c. \(\left(\frac{1}{1/2}\right)^2 = 4\)