![]() ![]() (constructive) 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 is d sin θ = mλ, for m = 0, 1, −1, 2, −2. If this distance equals an integral number of wavelengths, the rays all arrive in phase, and constructive interference (a maximum) is obtained. 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.Īs seen in Figure 5, each ray travels a distance d sin θ different from that of its neighbor, where d is the distance between slits. 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 Figure 5. As we know from our discussion of double slits in 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 5). 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. Tiny, finger-like structures in regular patterns act as reflection gratings, producing constructive interference that gives the feathers colors not solely due to their pigmentation. Natural diffraction gratings occur in the feathers of certain birds. ![]() ![]() Figure 4 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 2, and for reflection of light, as on butterfly wings and the Australian opal in Figure 3 or the CD in 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 2). (credit: Infopro, Wikimedia Commons)Īn interesting thing happens if you pass light through a large number of evenly spaced parallel slits, called a diffraction grating. Colors such as these are direct evidence of the wave character of light. The colors reflected by this compact disc vary with angle and are not caused by pigments. ![]()
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