The speed of light
During the seventeenth century, the question of whether light was a stream of particles or a rapid undulation of ethereal matter was unresolved. In any case, scientists generally agreed that light’s speed of propagation was exceedingly large. The fact that its propagation speed was indeed finite was determined in 1676 by Olaf Roemer (1644–1710), as follows. Roemer measured the period of the moon Io in its orbit around Jupiter (Figure 7). Io, orbiting Jupiter, acts like a clock. Roemer measured the period of this moon by timing how long it takes for the moon to make one full revolution of Jupiter, that is, the time between one eclipse and the next. When the earth was closest to Jupiter, Roemer found this period to be approximately 42.5 days. As the earth traveled in its orbit and away from Jupiter, Roemer predicted that successive eclipses would occur (as seen from earth) every 42.5 days as well. However, Roemer found that such eclipses occurred later and later, until after six months, when the earth was at the point most distant from Jupiter, Io’s eclipse was too late by a sizable time lag, which in modern figures is about 1000 s.
Jupiter and earth both revolve around the Sun. Because one Jupiter year is so much greater than one earth year, let us neglect Jupiter’s motion and consider it stationary. Also let us neglect earth’s elliptically shaped orbit, and for simplicity’s sake, let’s consider that the earth rushes in a straight line away from Jupiter for six months and then rushes directly back toward Jupiter during the remaining six months of the year. The distance traversed by earth during this hypothetical outward path is thus the diameter of the earth’s orbit, and the same distance is covered in the reverse path. In Roemer’s time, the diameter of the earth’s orbit was not known as accurately as it is today, so for the sake of this discussion, we use the modern figure of 300,000,000 km.
Roemer reasoned that the time lag of 1000 s represents the additional time that it takes for light from Jupiter’s moon to travel the extra distance across the diameter of the earth’s orbit. Thus, Roemer was the first person to show that the velocity of light is finite. In 1676, Roemer announced his discovery at a lecture at the Académie des Sciences. Christiaan Huygens (1629–1695) wrote to Roemer on 16 September 1677, asking for more information. Roemer’s discovery was a godsend because the finiteness of the velocity of light is essential to the workings of Huygens’ principle. Using Roemer’s data, Huygens was the first person to determine the velocity of light. In other words, Huygens performed the calculation
which says that the diameter divided by the time lag equals the velocity of light, c. (Note that we are using accurate numbers here, not the inaccurate ones of the seventeenth century.) Huygens gave full acknowledgment to Roemer. Huygens wrote, “But that which I only employed as an hypotheses, has recently received great verisimilitude as an established truth by the imaginative proof of Mr. Roemer” (Huygens, 1690). Such a great speed of light was almost unimaginable, and not surprisingly, it took about 50 years for Roemer’s demonstration to gain full acceptance. From then on, however, increasingly accurate measurements of the speed of light were obtained from ingenious experiments.
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Also in this chapter
- Wavefronts and raypaths
- d’Alembert’s solution
- One-dimensional waves
- Sinusoidal waves
- Phase velocity
- Wave pulses
- Geometric seismology
- Huygens’ principle
- Reflection and refraction
- Ray theory
- Fermat’s principle
- Fermat’s principle and reflection and refraction
- Appendix A: Exercise
- Huygens, C., 1690, Traité de la Lumière [Treatise on Light, in which are explained the causes of that which occurs in reflection and in refraction, and particularly in the strange refraction of Iceland Crystal]: The Hague. Republished by Macmillan and Company, London, 1912.
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