Telescopes and spectrographs

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# 2.1.2 Diffraction and interference of light

When light, or indeed any type of wave, passes through a narrow aperture, it will spread out on the other side. This is the phenomenon of diffraction. For example Figure 17 shows the diffraction of water waves in a device called a ripple tank. The extent to which waves are diffracted depends on the size of the aperture relative to the wavelength of the waves. If the aperture is very large compared to the wavelength, then the diffraction effect is rather insignificant. So although sound waves may be diffracted by a doorway, light waves are not appreciably diffracted by doorways because the wavelength of visible light (about 400 to 700 nm) is very small in comparison to the width of the doorway. But light is diffracted, and provided the slit is narrow enough, the diffraction will become apparent.

Figure 17 The diffraction of water waves in three different cases. As the slit width is reduced, the amount of diffraction increases

The phenomenon of diffraction allows us to appreciate the effect of an aperture on the propagation of waves, however it says nothing about what will happen when waves from different sources or from different parts of the same source meet. For this, the principle of superposition must be used. The principle of superposition states that if two or more waves meet at a point in space, then the net disturbance at that point is given by the sum of the disturbances created by each of the waves individually. For electromagnetic radiation the disturbance in question can be thought of as variations in electric and magnetic fields. The effect of the superposition of two or more waves is called interference.

To begin with, we consider the diffraction of monochromatic light by a pair of closely spaced, narrow slits as shown in Figure 18. Plane waves of constant wavelength from a single, distant, source are diffracted at each of two slits, S1 and S2. Because the waves are from the same original source they are in phase with each other at the slits. At any position beyond the slits, the waves diffracted by S1 and S2 can be combined using the principle of superposition. In the case of light waves, the resulting illumination takes the form of a series of light and dark regions called interference fringes and the overall pattern of fringes is often referred to as a diffraction pattern. (Note, however, that the same pattern is also sometimes referred to as an interference pattern. The reason for the dual nomenclature is that both diffraction and interference are necessary in order to generate the observed pattern, so either is an appropriate description.)

Figure 18 (a) Diffraction and interference of light produced by two narrow slits S1 and S2. (b) Bright and dark interference fringes on the screen

In order to appreciate how the interference fringes arise consider Figure 18a. When the wave arriving at a point on the screen from slit S1 is in phase with the wave arriving from S2, the resultant disturbance will be the sum of the disturbances caused by the waves individually and will therefore have a large amplitude (as shown in Figure 19a). This is known as constructive interference. When the waves are completely out of phase, the two disturbances will cancel. This is known as destructive interference (as shown in Figure 19b). On the screen, constructive interference will cause relatively high intensity, while destructive interference will lead to low intensity, hence the observed pattern of fringes.

Figure 19 (a) Constructive and (b) destructive interference

The general condition for constructive interference at any point is that the path difference between the two waves is a whole number of wavelengths, i.e.

The general condition for destructive interference is that the path difference is an odd number of half-wavelengths, i.e.

The result of this is that when a source of light consisting of a range of wavelengths is used, the positions of constructive interference will be different for each wavelength. In other words, the combination of diffraction and interference produced by a pair of slits has the effect of dispersing light into its constituent wavelengths.

The same principles also apply when not two but a large number of equally spaced slits are used. Such diffraction gratings typically have several hundred slits per millimetre and give much sharper diffraction patterns than a simple double slit. The individual fringes can also be much further apart, so that dispersed wavelengths can be more widely separated. The details of this phenomenon, as applied to astronomical spectroscopy, are discussed below.

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