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Learning objectives

By the end of this section, you will be able to:

  • Discuss the pattern obtained from diffraction grating.
  • Explain diffraction grating effects.

The information presented in this section supports the following AP® learning objectives and science practices:

  • 6.C.3.1 The student is able to qualitatively apply the wave model to quantities that describe the generation of interference patterns to make predictions about interference patterns that form when waves pass through a set of openings whose spacing and widths are small, but larger than the wavelength. (S.P. 1.4, 6.4)

An interesting thing happens if you pass light through a large number of evenly spaced parallel slits, called a diffraction grating    . An interference pattern is created that is very similar to the one formed by a double slit (see [link] ). 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. These can be photographically mass produced rather cheaply. Diffraction gratings work both for transmission of light, as in [link] , and for reflection of light, as on butterfly wings and the Australian opal in [link] or the CD pictured in the opening photograph of this chapter, [link] . In addition to their use as novelty items, diffraction gratings are commonly used for spectroscopic dispersion and analysis of light. What makes them particularly useful is the fact that they form a sharper pattern than double slits do. That is, their bright regions are narrower and brighter, while their dark regions are darker. [link] shows idealized graphs demonstrating the sharper pattern. Natural diffraction gratings occur in the feathers of certain birds. 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. This is called iridescence.

On the left side of the figure is a diffraction grating represented by a vertical bar with five horizontal slits cut through it. A single horizontal arrow, representing white light, points at the center slit from the left side. On the right side, five arrows spread symmetrically above and below the horizontal centerline. The arrow that is on the horizontal centerline points at a white block labeled central white. The first arrows above and below the centerline point to rainbow-colored blocks labeled first-order rainbow. The second arrows above and below the centerline point to slightly faded rainbow-colored blocks that are labeled second-order rainbow.
A diffraction grating is a large number of evenly spaced parallel slits. (a) Light passing through is diffracted in a pattern similar to a double slit, with bright regions at various angles. (b) The pattern obtained for white light incident on a grating. The central maximum is white, and the higher-order maxima disperse white light into a rainbow of colors.
Colorful photos of an Australian opal and a butterfly. The opal is full of fiery reds and yellows and deep blues and purples. The butterfly has its yellow wings spread and you can see its characteristic red, blue, and black spots and fringing.
(a) This Australian opal and (b) the butterfly wings have rows of reflectors that act like reflection gratings, reflecting different colors at different angles. (credits: (a) Opals-On-Black.com, via Flickr (b) whologwhy, Flickr)
The upper graph, which is labeled double slit, shows a smooth curve similar to a sine curve that is shifted up so that its minimum value is zero. Three peaks are shown: the middle peak is labeled m equals zero and the left and right peaks are labeled m equals one. The lower graph, which is labeled grating, is aligned under the upper graph and also shows three peaks, with each peak aligned directly underneath the peaks in the upper graph. These three peaks are also labeled m equals zero or one, as in the upper graph. However, the peaks in the lower graph are much narrower and there are lots of small peaks appearing between large peaks.
Idealized graphs of the intensity of light passing through a double slit (a) and a diffraction grating (b) for monochromatic light. Maxima can be produced at the same angles, but those for the diffraction grating are narrower and hence sharper. The maxima become narrower and the regions between darker as the number of slits is increased.

The analysis of a diffraction grating is very similar to that for a double slit (see [link] ). 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. Rays traveling in the same direction (at an angle θ size 12{θ} {} relative to the incident direction) are shown in the figure. Each of these rays travels a different distance to a common point on a screen far away. 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. As seen in the figure, each ray travels a distance d sin θ size 12{d`"sin"θ} {} different from that of its neighbor, where d size 12{d} {} is the distance between slits. If this distance equals an integral number of wavelengths, the rays all arrive in phase, and constructive interference (a maximum) is obtained. Thus, the condition necessary to obtain constructive interference for a diffraction grating    is

Practice Key Terms 2

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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