Visible light is a particular type of electromagnetic radiation and travels through space in the form of a wave. A wave is characterized by the wave period, the length of time taken for one complete cycle; the wavelength, the distance between successive wave crests; and the wave amplitude, which measures the size of the disturbance associated with the wave. The wave frequency is simply 1 divided by the wave period—it counts the number of wave crests that pass a given point in one second. Diffraction is the tendency of a wave to spread out after passing through an opening or to bend around a corner. Interference is the ability of two waves to reinforce or partially cancel each other.

Electrons and protons are elementary particles that carry equal and opposite electrical charges. Any electrically charged object is surrounded by an electric field that determines the force it exerts on other charged objects. Like gravitational fields, electric fields decrease as the square of the distance from their source.

When a charged particle moves, information about that motion is transmitted throughout the universe by the particle's changing electric field. The information travels in the form of a wave at the speed of light. Both electric and magnetic fields are involved, so the phenomenon is known as electromagnetism.

A beam of white light is bent, or refracted, as it passes through a prism. Different frequencies of light within the beam are refracted by different amounts, so the beam is split up into its component colors—the visible spectrum. The color of visible light is simply a measure of its wavelength—red light has a longer wavelength than blue light. The entire electromagnetic spectrum consists of (in order of increasing frequency) radio waves, infrared radiation, visible light, ultraviolet radiation, X rays, and gamma rays.

The opacity of Earth's atmosphere—the extent to which it absorbs radiation—varies greatly with wavelength. Only radio waves, some infrared wavelengths, and visible light can penetrate the atmosphere and reach the ground from space.

The temperature of an object is a measure of the speed with which its constituent particles move. The intensity of radiation of different frequencies emitted by a hot object has a characteristic distribution, called a blackbody curve, that depends only on the temperature of the object. Wien's law tells us that the wavelength at which the object radiates most energy is inversely proportional to its temperature. Stefan's law states that the total amount of energy radiated is proportional to the fourth power of the temperature.

Our perception of the wavelength of a beam of light can be altered by our velocity relative to the source. This motion-induced change in the observed frequency of a wave is called the Doppler effect. Any net motion away from the source causes a redshift—a shift to lower frequencies—in the received beam. Motion toward the source causes a blueshift. The extent of the shift is directly proportional to the observer's radial velocity relative to the source.


1. Light, radio, ultraviolet, and gamma rays are all forms of electromagnetic radiation. HINT

2. Sound is a familiar type of electromagnetic wave. HINT

3. The amount of diffraction increases with increasing wavelength.

4. Interference occurs when one wave is brighter than another; the fainter wave cannot be observed.

5. Electromagnetic waves cannot travel through a perfect vacuum. HINT

6. Electromagnetic waves all travel at the same speed, the speed of light. HINT

7. Visible light makes up the greatest part of the entire electromagnetic spectrum. HINT

8. Ultraviolet light has the shortest wavelength of any electromagnetic wave. HINT

9. A blackbody emits all its radiation at one wavelength or frequency. HINT

10. A perfect blackbody emits exactly as much radiation as it absorbs from outside. HINT

11. The shape of a blackbody curve depends on the temperature of the body. HINT

12. The frequency at which the blackbody curve peaks increases with temperature. HINT

13. Objects moving away from an observer are redshifted because they actually turn red. HINT

14. The Doppler effect occurs for all types of wave motion. HINT

15. An object emitting radiation, moving transverse to the line of sight, produces no Doppler effect. HINT


1. The speed of light is _____ km/s. HINT

2. The _____ of a wave is the distance between any two adjacent wave crests.

3. The _____ of a wave is measured in units of hertz (Hz).

4. _____ is the ability of a wave to "bend around corners."

5. When a charged particle moves, information about this motion is transmitted through space by means of its changing _____ and _____ fields. HINT

6. The visible spectrum ranges from _____ to _____ in wavelength. HINT

7. Light with a wavelength of 700 nm is perceived to be _____ in color. HINT

8. Earth's atmosphere has low opacity for three forms of electromagnetic radiation. They are _____, _____, and _____. HINT

9. The peak of an object's emitted radiation occurs at a frequency or wavelength determined by the object's _____. HINT

10. The lowest possible temperature is _____ K. HINT

11. Water freezes at _____ K. HINT

12. Because the Sun emits its peak amount of radiation at about 480 nm, its temperature must be about _____ K.

13. Two identical objects have temperatures of 1000 K and 1200 K, respectively. It is observed that one of the objects emits twice as much radiation as the other. Which one is it? _____. HINT

14. If an astronomical object is observed to emit X-rays, it is reasonable to assume its temperature is very _____. HINT

15. When an observer and/or an object emitting radiation move toward each other, the observer sees the radiation shifted to _____ wavelengths. HINT


1. Define the following wave properties: period, wavelength, amplitude, frequency.

2. What is the relationship between wavelength, wave frequency, and wave velocity?

3. What is diffraction, and how does it relate to the behavior of light as a wave?

4. What's so special about c?

5. Compare and contrast the gravitational force with the electric force. HINT

6. Describe the way in which light radiation leaves a star, travels through the vacuum of space, and finally is seen by someone on Earth. HINT

7. Name the colors that combine to make white light. What is it about the various colors that causes us to perceive them differently? HINT

8. What do radio waves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays have in common? How do they differ? HINT

9. In what regions of the electromagnetic spectrum is the atmosphere transparent enough to allow observations from the ground? HINT

10. What is a blackbody? What are the characteristics of the radiation emitted by a blackbody?

11. What does Wien's law reveal about stars in the sky? HINT

12. What does Stefan's law tell us about the radiation emitted by a blackbody? HINT

13. In terms of its blackbody curve, describe what happens as a red-hot glowing coal cools off. HINT

14. What is the Doppler effect, and how does it alter the way in which we perceive radiation? HINT

15. If Earth were completely blanketed with clouds and we couldn't see the sky, could we learn about the realm beyond the clouds? What other forms of radiation might be received? HINT


1. A sound wave moving through water has a frequency of 256 Hz and a wavelength of 5.77 m. What is the speed of sound in water?

2. What is the wavelength of a 100-MHz ("FM 100") radio signal?

3. What would be the frequency of an electromagnetic wave having a wavelength equal to Earth's diameter? In what part of the electromagnetic spectrum would such a wave lie?

4. According to Wien's law, how many times hotter is an object whose blackbody emission spectrum peaks in the ultraviolet, at a wavelength of 200 nm, than an object whose spectrum peaks in the red, at 650 nm? According to Stefan's law, how much more energy does it radiate per unit area per second?

5. Normal human body temperature is about 37°C. What is this temperature in kelvins? What is the peak wavelength emitted by a person with this temperature? In what part of the spectrum does this lie? HINT

6. The Sun has a temperature of 5800 K, and its blackbody emission peaks at a wavelength of approximately 550 nm. At what wavelength does a protostar with a temperature of 1000 K radiate most strongly?

7. Two otherwise identical bodies have temperatures of 300 K and 1500 K, respectively. Which one radiates more energy, and by what factor does its emission exceed the emission of the other body? HINT

8. According to Stefan's law, how much energy is radiated into space per unit time by each square meter of the Sun's surface (see More Precisely 3-2)? If the Sun's radius is 696,000 km, what is the total power output of the Sun? HINT

9. At what radial velocity, and in what direction, would a spacecraft have to be moving for a radio station transmitting at 100 MHz to be picked up by a radio tuned to 99.9 MHz? HINT

10. Imagine you are observing a spacecraft moving in a circular orbit of radius 100,000 km around a distant planet. You happen to be located in the plane of the spacecraft's orbit. You find that the spacecraft's radio signal varies periodically in wavelength between 2.99964 m and 3.00036 m. Assuming that the radio is broadcasting normally, at a constant wavelength, what is the mass of the planet? HINT


1. Locate the constellation Orion. Its two brightest stars are Betelgeuse and Rigel. Which of these is the hotter star? Which is cooler? How can you tell? Which of the other stars scattered across the night sky are hot, and which are cool?

2. Stand near (but not too near!) a train track or busy highway and wait for a train or traffic to pass by. Can you notice the Doppler effect in the pitch of the engine noise or whistle blowing? How does the sound frequency depend on (a) speed? (b) the motion toward or away from you?