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Light is a traveling transverse wave in an oscillating electric and magnetic field. The speed of light in a vacuum is a constant at 3×108 m/s. The colors of visible light are directly related to the wavelength of the light. Light can be scattered by small particles, but scattering of light waves depends on the relative sizes of the particles and the wavelength of the light. This is similar to the idea that long-wavelength water waves can easily pass around small boulders but short-wavelength water waves cannot. Scattering of light is the explanation for why the daytime sky is blue and sunsets are red. 
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light, electromagnetic wave, speed of light, vacuum, scattering
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Review problems and questions |
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- Use a diagram and describe with words the connection between the field of an electric charge and light waves.
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An oscillating electric field, such as can be produced with an oscillating electric charge, can generate light waves. 
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- Lightning strikes a tree one mile (1.609 km) away from you. Light from the lightning bolt travels at 3×108 m/s while sound waves from the accompanying thunderclap travel at about 343 m/s.
- How long does it take the light to reach you?
- How long does it take the sound of the thunderclap to reach you?
- Formulate a simple rule for estimating the distance to a lightning strike.
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- Light takes 5.4×10−6 s.
- Sound takes 4.7 s.
- The light arrives almost instantaneously, but the sound takes roughly five seconds per mile of distance. To estimate the distance to a lightning strike, count the seconds between the sight of the lightning bolt and the sound of the thunder and divide by five to find the distance in miles.
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- How are electromagnetic waves similar to sound waves? How are they different?
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Sound waves require a medium to propagate, whereas electromagnetic waves do not (they can travel through a vacuum).
Both kinds of waves transport energy from one place to another.
Both kinds of waves change their speed when they propagate through a different medium.
Electromagnetic waves are transverse; sound is a longitudinal wave.
The speed of light waves is much faster than the speed of sound waves.
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- How are the electric and magnetic fields in an electromagnetic wave related to each other?
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The electric and magnetic fields in an electromagnetic wave are always perpendicular to each other. They also propagate in phase, meaning that the electric field increases at the same time that the magnetic field increases.
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- Which has higher frequency, cyan light or yellow light?
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Cyan has a higher frequency, which you can see from the interactive simulation on page 634.
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- What is the frequency of light with a wavelength of 560 nm?
- An angstrom (Å) is 10−10 m. What wavelength, in nanometers, corresponds to 6,563 Å?
- What is the wavelength of light corresponding to 121.5 MHz?
- Which has a higher frequency, light with a wavelength of 1.7 μm or light with a frequency of 7.3×1013 Hz?
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Answer: - The frequency is 5.4×1014 Hz.
- 6,563 Å = 656.3 nm.
- The wavelength is 2.47 m.
- 1.7 μm light has a higher frequency.
Solution: - Calculate using the frequency equation:
- Since one angstrom is 10−10 m and one nanometer is 10−9 m, you convert one to the other by a factor of 10: 6,563 Å = 656.3 nm.
- Convert the frequency: 121.5 MHz = 121.5×106 Hz = 1.215×108 Hz. Then calculate the wavelength: This radio frequency is the civilian emergency band for aircraft communications.
- Calculate the frequency of light that has a wavelength of 1.7 μm: This is a higher frequency than 7.3×1013 Hz.
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- Imagine looking up at the night sky. If you look in any given direction at a tiny patch of sky, you will eventually come across a star or galaxy. That little patch of sky would then appear white. The German astronomer Heinrich Wilhelm Olbers in 1823 described this as a paradox: Why is the night sky black instead of white? Offer an explanation to resolve this paradox.
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The assumption is that, if the universe is infinitely large and populated throughout with stars and galaxies, you would eventually come across a star or galaxy in any little patch of sky. The resolution to Olber’s Paradox is that the universe is not infinitely large, but instead it has a limited extent.
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- If we were on a planet—or moon—that had no atmosphere, what color would the daytime sky be?
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The daytime sky would be black if there was no atmosphere. For the daytime sky to be any color (other than black, the absence of color), there must be scattering of sunlight!
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