Light

It is now known that under all common circumstances light behaves as a wave propagating at a speed close to 300,000km/s. This, however, is a recent realization; in fact, whether light traveled at finite or infinite speed was the subject of much debate was left unanswered for a long time. Galileo tried to measure the speed of light by experiment: he put two persons on hills (separated by a bit less than a mile), and then told one open a lantern, the other was to raise his/her hand when he/she sees the light and the first notes any lapse between his/her opening the lantern and seeing the raised hand. No time delay was observed (which is not unnatural, the lapse is about 10^-5s!). So the question remained unanswered

In 1670 the Danish mathematician Olaus Rømer observed that the eclipses of Jupiter's moons were 11 minutes ahead of schedule when the Earth was closer to Jupiter, and they lagged behind (also by 11 minutes) when the Earth was farthest from Jupiter. Assuming that there are no problems with the predictions of Newtonian physics concerning the motion of Jupiter's moons, he concluded that the discrepancy was due to the different times light takes to get to Earth at the two extremes of its orbit (Jupiter moves very little during one year, it takes 12 years for it to circle the sun), see Fig. 5.2. Rømer then calculated that the speed of light would be 210,000km/s. The modern value of the speed of light is 299,792km/s.

This is, of course, not the only possible explanation, Rømer could have argued, for example, that Newton's equations could not account for Jupiter's motion. Still the hypothesis that light travels at a finite speed furnished the simplest explanation and, following Ockham's razor (Sect. 1.2.5) it is the one which ought to be examined first. Soon after Rømer's argument was made public the fact that light travels at finite speed was demonstrated in various experiments and was universally accepted.

**Figure 5.2:** Diagram of the reasoning used by Rømer to determine the speed of light.
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So light propagates at a finite speed. What is it made of? Newton believed that light was made of corpuscles, but even the weight of Newton's opinions could not withstand the experimental evidence showing that light behaves as a wave. This sounds preposterous: a wave, such as sound, will ``go around corners'' but light does nothing of the kind...or does it? In fact, it does! If you look very closely at a very sharp edged screen you will see that some light actually goes behind the screen: light does behave as a wave (see Fig. 5.3). This is not common knowledge because it is a small effect, light dies out almost as it turns the corner, if the corner is not very sharp, light is scattered in many ways and the effects disappears; in other words, for light, almost any obstruction is a very tall wall.

**Figure 5.3:** Picture of the shadow cast by the corner of a screen. Note that the shadow region is not completely dark.
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The wave theory of light leads to some surprising consequences. For example, it predicts that the shadow cast by a dark circular screen should have a bright spot in its center, and this would be absurd were it not for the fact that the bright spot is indeed there! (see Fig: 5.4)

**Figure 5.4:** Shadow cast by a small opaque disk. Note the bright spot in the center of the shadow.
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By the beginning of the 19th century the hypothesis that light is a wave traveling at large (by our standards) but finite speed

was proven and was universally accepted. Being a wave we can ask what is its wavelength, amplitude, frequency, etc; it turns out that visible light has very small wavelength, about 10^-5cm. Another natural question is then, do electromagnetic waves with larger and smaller wavelengths exist?

The answer is yes. Visible light is but a member of a large family of waves; they are all electromagnetic waves, and they are all described by the Maxwell's equations. For historical reasons waves of different wavelengths have different names (see Fig. 5.5). Thus we have (the symbol ~ means ``about'')

**Figure 5.4:** Shadow cast by a small opaque disk. Note the bright spot in the center of the shadow.
2\|c\|Wavelengths of electromagnetic waves
Name	Wavelength
Radio	~ 10 cm or larger
Microwave	~ 1 cm
Infrared	~ 10^-3cm
Visible	~ 10^-5cm
Ultraviolet	~ 10^-6cm
X-rays	~ 10^-8cm
Gamma-rays	~ 10^-9cm or smaller

**Figure 5.5:** The electromagnetic spectrum.
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All of these are common names. Every one of these waves travels at the same speed in vacuum

equal to the speed of light (called ``visible'' above) in vacuum; the only difference between them is the wavelength, the distance between two consecutive crests in the corresponding wave trains.

So light is a wave, similar then to sound waves, or water waves. But all these waves are produced by the undulations of some medium: water for water-waves, air (for example) for sound, etc. Thus it was postulated that the medium in which light undulates is called ether.