Diffraction grating showing light rays from each slit traveling in the same direction. However, the slits are usually closer in diffraction gratings than in double slits, producing fewer maxima at larger angles. Note that this is exactly the same equation as for double slits separated by d. Where d is the distance between slits in the grating, λ is the wavelength of light, and m is the order of the maximum. Thus, the condition necessary to obtain constructive interference for a diffraction grating isĭ sinθ = m λ for m = 0, 1, -1, 2, -2, 3, -3 … (constructive) If this distance equals an integral number of wavelengths, the rays all arrive in phase, and constructive interference (a maximum) is obtained. As seen in the figure, each ray travels a distance dsinθ different from that of its neighbour, where d is the distance between slits. The rays start in phase, and they can be in or out of phase when they reach a screen, depending on the difference in the path lengths traveled. Each of these rays travels a different distance to a common point on a screen far away. Rays traveling in the same direction (at an angle θ relative to the incident direction) are shown in the figure. As we know from our discussion of double slits in Chapter Young’s Double Slit Experiment, light is diffracted by each slit and spreads out after passing through. The analysis of a diffraction grating is very similar to that for a double slit (see Figure 4). The maxima become narrower and the regions between darker as the number of slits is increased. Maxima can be produced at the same angles, but those for the diffraction grating are narrower and hence sharper. Idealized graphs of the intensity of light passing through a double slit (a) and a diffraction grating (b) for monochromatic light. (credits: (a), via Flickr (b) whologwhy, Flickr) Figure 3. (a) This Australian opal and (b) the butterfly wings have rows of reflectors that act like reflection gratings, reflecting different colours at different angles. The central maximum is white, and the higher-order maxima disperse white light into a rainbow of colours. (b) The pattern obtained for white light incident on a grating. (a) Light passing through is diffracted in a pattern similar to a double slit, with bright regions at various angles. A diffraction grating is a large number of evenly spaced parallel slits. Tiny, finger-like structures in regular patterns act as reflection gratings, producing constructive interference that gives the feathers colours not solely due to their pigmentation. Natural diffraction gratings occur in the feathers of certain birds. Figure 3 shows idealized graphs demonstrating the sharper pattern. That is, their bright regions are narrower and brighter, while their dark regions are darker.
What makes them particularly useful is the fact that they form a sharper pattern than double slits do. In addition to their use as novelty items, diffraction gratings are commonly used for spectroscopic dispersion and analysis of light. Diffraction gratings work both for transmission of light, as in Figure 1, and for reflection of light, as on butterfly wings and the Australian opal in Figure 2 or the CD pictured in the opening photograph of this chapter, Figure 1. These can be photographically mass produced rather cheaply. A diffraction grating can be manufactured by scratching glass with a sharp tool in a number of precisely positioned parallel lines, with the untouched regions acting like slits. An interference pattern is created that is very similar to the one formed by a double slit (see Figure 1). Discuss the pattern obtained from diffraction grating.Īn interesting thing happens if you pass light through a large number of evenly spaced parallel slits, called a diffraction grating.
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