![]() Also notice that the maximum intensity of the double slit is 4 units, the 3-slit case has a maximum intensity of 9 units, and for 4-slits it is 16 units, as we expect when the amplitude increases by one unit with the addition of each slit. Notice that the bright fringes for any number of slits occur at the same places as for the double slit (provided they have the same slit separation), and that the number of dark fringes between bright fringes goes up by one every time another slit is added. Putting these functions into a graphing calculator confirms what we found above, as well as what we suspect about \(n\) slits – that there are \(n-1\) dark fringes between each maximally-bright fringe.įigure 3.3.3 - Comparison of Interference Patterns by Number of Slits As we know from our discussion of double slits in Chapter 27.3 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 colors at different angles. ![]() The central maximum is white, and the higher-order maxima disperse white light into a rainbow of colors. ![]() (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 colors 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, Chapter 27 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. In this limit, the ratio kx, 2 / z is negligibly small for all values of x under the integral, and we can approximate it as. (i) Fraunhofer diffraction takes place when z / a > a / the relation which may be rewritten either as a < < (z)1 / 2, or as ka2 < < z. I will show you how to derive the diffraction grating formula step by step. It may be simplified in the following two (opposite) limits. An interference pattern is created that is very similar to the one formed by a double slit (see Figure 1). Grating formula physics 4.4 Diffraction Gratings - University Physics Volume. 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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