## Diffraction gratings

For light coming from two slits, the image is a set of broad bright and dark bands. If the number of slits is increased, the condition for constructive interference, d sin 6 = mk, applies to all pairs of adjacent slits.

The points of maximum intensity are in exactly the same positions on the screen for any number of slits provided that adjacent slits are separated by the same distance and that the experimental arrangement is the same. As the number of slits is increased, more light is transmitted and that light becomes concentrated into narrower bright bands, as illustrated in Figure 8.14.

A diffraction grating (which could equally well be called an interference grating) has typically tens of thousands of slits and the maxima form extremely narrow lines. Diffraction gratings disperse light because different wavelengths interfere constructively at different angles.

Bright lines are found at all angles where sin 0 = m

2 slits

10 slits

100 slits

10 slits

100 slits

Figure 8.14 Maxima occur in the same place regardless of the number of slits.

Figure 8.14 Maxima occur in the same place regardless of the number of slits.

intensity m = 0

Figure 8.15 Spectrum of an imaginary source with three strong emission lines.

The colour of the zero order bright line reflects the relative intensities of the lines in the spectrum because all the light is in phase there (light from a sodium lamp is orange because of the 'sodium doublet', a pair of strong emission lines at 589.0 nm and 589.6 nm).

Figure 8.15 represents the spectrum of an imaginary source with three strong atomic emission lines. The spectral lines are better separated as m increases but higher order lines are less intense because individual slits have a finite width.

Light is emitted when atomic electrons make transitions between allowed energy levels. Each atom has its own characteristic spectrum — its 'fingerprint'. Heavy atoms have more complex spectra than light atoms; in molecular spectra, some lines may smear into bands. In general, the more tightly bound the atom, the more complex the spectrum. Diffraction gratings enable us to make the high precision measurements of wavelength that are needed for analysis of the properties of what may be very complex materials.

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