PHY104 - Introduction to Astrophysics

PHY104 - Introduction to Astrophysics S. P. Littlefair June 4, 2013 Chapter 1 Properties of Light 1.1 Introduction The only information we have about our Universe comes from the light emitted by objects within it. A good understanding of light is essential in all of astrophysics. We must learn what light is and how it behaves. We must understand it's properties, and learn how to use those properties to discover the information we seek. Finally, we must understand how light interacts with the matter around it. Much of the rest of the astrophysics course at Sheffield deals with what we know. By covering the basic physics of light, this course aims to explain how we acquire that knowledge. Our starting point is a question which seems quite simple; \what is light"? 1.2 The wave nature of light It is easy to demonstrate that light behaves like a wave. The famous Young's slit experiment is an elegant demonstration, and is shown in the left-hand side of figure 1.1. In this experiment, a thin plate with two parallel slits are illuminated by a single light source, and the light passing through the slits strikes a screen behind them. When we look on the screen, we see a diffraction pattern, made up of a series of bright and dark fringes. The diffraction pattern is easily understood if we think of light as a wave propa- gating through some medium, like water waves on a lake. In our experiment, each slit acts as a source of light waves; a wavefront of light spreads out from each slit. The two wavefronts of light hit the screen, and the brightness of light at that point depends on how the wavefronts interfere. If the light waves are in phase (if the peaks of both waves line up), then we get a bright 1 Figure 1.1: Left: A schematic of the Young's double slit experiment. A light source behind S1 illuminates the two slits at S2. These slits act as secondary sources of light, and light waves spread out from the slits like water waves on a lake. Right: the principle of superposition. Light in phase adds to give brighter light, but light which is out of phase cancels out to produce dark regions. region. If the two waves are out of phase (the peak of one wave corresponds to a trough in the other), the light waves cancel out, and we see a dark region (see RHS of figure 1.1). We will return to the wave nature of light in a moment, but first let us look at the startling property of light that emerges from quantum mechanics. 1.3 The particle nature of light Whilst it is easy to demonstrate that light behaves like a wave, it is also possible (though nowhere near as easy!) to demonstrate that light behaves like a particle. When a metal plate is illuminated with blue or ultraviolet light, electrons absorb the energy from the light, and can escape from the metal. This phenomenon is known as the photoelectric effect. If light is a wave, we might think that the energy of the escaping electrons would increase as the intensity of light increased, but the frequency of that light wouldn't matter. In fact, the energy of the released electrons increases in proportion to the frequency of the light, and below a certain frequency, no electrons are emitted from the metal at all (see figure 1.2). It is extremely difficult to explain this result by thinking about light as a wave. The photoelectric effect’s dependence upon frequency was predicted by Einstein, in 1905, based upon a model of light as particles of light, called 2 e- ν Energy E=hν - hν0 ν0 Frequency Figure 1.2: The photoelectric effect. Blue light is shone onto a metal plate. Electrons in the metal absorb the energy from the light and escape from the metal (left hand side). When the energy of the emerging electrons is measured, it turns out to be proportional to the frequency of the light (right hand side). Furthermore, below a certain frequency, no electrons are released from the metal plate. This effect led Einstein to propose the particle nature of light in 1905. photons. He suggested that each photon has an energy which is proportional to its frequency, E = hν. An electron requires a certain amount of energy to free it from the metal. If we call this amount of energy W (known as the work function) then the energy of the freed electron should be given by Enu = hν −W . Thus, the energy of the emerging electron is proportional to the frequency of the incident light, just as we see in the photoelectric effect. What happens if the frequency of the light is reduced, so that the energy carried by the photons is less than W ? In this case, no single photon has enough energy to liberate an electron, and so no electrons can escape the metal. These were the predictions made by Einstein for the behaviour of the photoelectric effect. Einstein's predictions of the frequency dependence of the photoelectric effect, based upon the photon model, were confirmed in painstaking experiments by Millikan in 1913-1914. Although Millikan didn't believe in the particle nature of light at the time, his experiments earned him the Nobel prize, and gave tremendous support to the picture of light as discrete particles of light. The photoelectric effect tells us that each photon has an energy given by E = hν. Photons also have a momentum, given by p = E=c = hν=c, although to understand why requires us to study Einstein's theory of special 3 relativity, which is beyond this course. 1.4 The wave-particle nature of light So we have some experiments which show that light behaves as a wave, and other which show quite clearly that light behaves as a particle. In fact, there are even experiments that show that light can behave as both a particle and a wave at the same time! We are going to go back to the Young's slit experiment described earlier, but perform an experiment in which we reduce the intensity of the light so much that only one photon illuminates the plate with the slits at any one time. Now, let us put a special camera in place of the screen, that can detect each photon as it arrives at the screen. What we find is astonishing. The light is clearly behaving like photons, because we see each one hit the screen individually. The location of each photon as it hits the screen is seemingly random; one photon arrives at a given location and a moment later another photon arrives somewhere else. Over time, however, as we watch the photons arrive one-by-one, we find more photons are hitting the screen where the bright regions of the original diffraction pattern were! How can this be? The diffraction pattern was made by the interference of waves of light. The photons are going through the slit one- by-one and so cannot be interfering with each other. What is going on is that the photons are interfering with themselves; behaving as a particle and a wave at the same time. Thus, whilst light sometimes behaves as a wave, and sometimes as a particle, in reality it is neither. The true nature of light is much stranger, and is given by quantum mechanics, which you will study later in the Physics course. In the remainder of this module, we will choose to describe light as either a particle or a wave, depending on which suits us most! 1.5 The electro-magnetic spectrum If light is a wave, what is it a wave in? The answer is that light is an electro- magnetic wave. Modern theory describes light as electric and magnetic fields which oscillate in phase, perpendicular to the velocity of propagation, but in planes oriented at 90 degrees to each other. Confused? Have a look at figure 1.3, or take a look at the JAVA applet at http://www.phys.hawaii. edu/~teb/java/ntnujava/emWave/emWave.html. Like any wave, it's speed of propagation is given by the wave equation, c = νλ, where c is the speed of light, ν is the frequency, and λ is the wave- 4 Figure 1.3: An electromagnetic wave. length of the light. Light of different frequencies is referred to by different names; visible light is only a tiny portion of the electro-magnetic spectrum, which is shown in figure 1.4. In astronomy one of the most useful techniques available to us is to exploit the full electro-magnetic spectrum. Because light is described both by the wave equation (c = νλ) and by E = hν, we can describe a position on the electro-magnetic spectrum by wavelength, frequency, or energy. Visible light (frequencies around 1015 Hz) tells us much about the thermal emission from stars and galaxies, but infrared and microwave radiation (wavelengths from 1 micron to 1 cm) can show us the location of very cool stars and dust, whilst high-energy radiation (γ-rays, X-rays and UV emission) tells us about the most energetic processes in the Universe. Only a small portion of the electromagnetic spectrum is observable from the surface of the Earth, however. The optical, infrared and radio portions of the spectrum are visible through atmospheric windows, but the Earth's atmosphere is opaque to other wavelengths of light. The transparency of the Earth's atmosphere is shown in figure 1.5.

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