24.3

The Speed of Light

At a speed of , light travels from the earth to the moon in a little over a second, so the time required for light to travel between two places on earth is very short. Therefore, the earliest attempts at measuring the speed of light had only limited success. One of the first accurate measurements employed a rotating mirror, and Figure 24-12 shows a simplified version of the setup. It was used first by the French scientist Jean Foucault (1819–1868) and later in a more refined version by the American physicist Albert Michelson (1852–1931). If the angular speed of the rotating eight-sided mirror in Figure 24-12 is adjusted correctly, light reflected from one side travels to the fixed mirror, reflects, and can be detected after reflecting from another side that has rotated into place at just the right time. The minimum angular speed must be such that one side of the mirror rotates one-eighth of a revolution during the time it takes for the light to make the round trip between the mirrors. For one of his experiments, Michelson placed his fixed and rotating mirrors on Mt. San Antonio and Mt. Wilson in California, a distance of 35 km apart. From a value of the minimum angular speed in such experiments, he obtained the value of in 1926.

Figure 24-12 Between 1878 and 1931, Michelson used a rotating eight-sided mirror to measure the speed of light. This is a simplified version of the setup.

Today, the speed of light has been determined with such high accuracy that it is used to define the meter. As discussed in Section 1.2, the speed of light is now defined to be

although a value of is adequate for most calculations. The second is defined in terms of a cesium clock, and the meter is then defined as the distance light travels in a vacuum during a time of 1/(299 792 458) s. Although the speed of light in a vacuum is large, it is finite, so it takes a finite amount of time for light to travel from one place to another. The travel time is especially long for light traveling between astronomical objects, as Conceptual Example 3 discusses.

| Conceptual Example 3 | | | Looking Back in Time

A supernova is a violent explosion that occurs at the death of certain stars. For a few days after the explosion, the intensity of the emitted light can become a billion times greater than that of our own sun. But after several years, the intensity usually returns to zero. Supernovae are relatively rare events in the universe, for only six have been observed in our galaxy within the past 400 years. One of them was recorded in 1987. It occurred in a neighboring galaxy, approximately away. Figure 24-13 shows a photograph of the sky (a) before and (b) a few hours after the explosion. Why do astronomers say that viewing an event like the supernova is like looking back in time?

Figure 24-13 A view of the sky (a) before and (b) a few hours after the 1987 supernova. (Courtesy Anglo-Australian Telescope Board)

Reasoning and Solution The light from the supernova traveled to earth at a speed of . Even at such a speed, the travel time is large because the distance is enormous. The time t is

This corresponds to 175 000 years. So when astronomers saw the explosion in 1987, they were actually seeing the light that left the supernova 175 000 years earlier; in other words, they were “looking back in time.” In fact, whenever we view any celestial object, such as a star, we are seeing it as it was a long time ago. The farther the object is from earth, the longer it takes for the light to reach us, and the further back in time we are looking.
Related Homework: Problem 14

In 1865, Maxwell determined theoretically that electromagnetic waves propagate through a vacuum at a speed given by

| (24.1)

where is the (electric) permittivity of free space and is the (magnetic) permeability of free space. Originally was introduced in Section 18.5 as an alternative way of writing the proportionality constant k in Coulomb’s law and, hence, plays a basic role in determining the strengths of the electric fields created by point charges. The role of is similar for magnetic fields; it was introduced in Section 21.7 as part of a proportionality constant in the expression for the magnetic field created by the current in a long, straight wire. Substituting the values for and into Equation 24.1 shows that

The experimental and theoretical values for c agree. Maxwell’s success in predicting c provided a basis for inferring that light behaves as a wave consisting of oscillating electric and magnetic fields.

Check Your Understanding 1

The frequency of electromagnetic wave A is twice that of electromagnetic wave B. For these two waves, what is the ratio of the wavelengths in a vacuum ? (a) , because wave A has twice the speed that wave B has. (b) , because wave A has one-half the speed that wave B has. (c) , because wave A has one-half the speed that wave B has. (d) because wave A has twice the speed that wave B has. (e) , because both waves have the same speed. (The answer is given at the end of the book.)
Background: Electromagnetic waves have a frequency f, wavelength , and speed v that are related according to (Equation 16.1).
For similar questions (including calculational counterparts), consult Self-Assessment Test 24.1, which is described at the end of Section 24.6.

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