Imagine that the slit is wide enough to allow a number of wavelets. The rays from A and B interfere at P on a distant screen. As shown, AP exceeds BP by half a wavelength; therefore, the represented waves destructively interfere. Also for every wave originating between A and B , there is another point between B and C with a wavelet that will destructively interfere.
The wavelets cancel in pairs; thus, point P is a minimum or dark point on the screen. The triangle ACD is nearly a right triangle if P is quite distant. Applying the definition for sine to the figure yields. Whenever the path difference between AP and CP is a whole number of wavelengths, a dark fringe will be produced on the screen because the wavelets can be seen to completely cancel in pairs.
Figure 2 illustrates the light rays traveling to another point on the screen. Diffraction patterns can be observed when light passes through a set of regularly spaced slits. For a diffraction to produce an observable pattern, the spacing of the slits must be comparable to the wavelength of the radiation.
This spacing is 4 to 8 times larger than the wavelengths of visible light and produces an easily observable pattern. The wavelengths of x-rays lie in the 1 nm to 1 pm range. A typical diffraction grating will not produce an observable pattern.
But the wavelengths of x-rays are comparable to the spacing of atoms in common crystals, and material with a regularly spaced grid of atoms can diffract x-rays and produce diffraction patterns that can be captured on photographic film. Water waves in a ripple tank A single large slit: A single small slit:. Diffraction is the tendency of a wave emitted from a finite source or passing through a finite aperture to spread out as it propagates.
Diffraction results from the interference of an infinite number of waves emitted by a continuous distribution of source points. According to Huygens' principle every point on a wave front of light can be considered to be a secondary source of spherical wavelets. These wavelets propagate outward with the characteristic speed of the wave. The wavelets emitted by all points on the wave front interfere with each other to produce the traveling wave.
Huygens' principle also holds for electromagnetic waves. When studying the propagation of light, we can replace any wave front by a collection of sources distributed uniformly over the wave front, radiating in phase.
Water waves in a ripple tank. A single large slit:. A single small slit:. The intensity is a function of angle. Huygens' principle tells us that each part of the slit can be thought of as an emitter of waves. All these waves interfere to produce the diffraction pattern. Where crest meets crest we have constructive interference and where crest meets trough we have destructive interference. Very far from a point source the wave fronts are essentially plane waves.
This is called the Fraunhofer regime , and the diffraction pattern is called Fraunhofer diffraction. The positions of all maxima and minima in the Fraunhofer diffraction pattern from a single slit can be found from the following simple arguments.
Consider a slit of width w, as shown in the diagram on the right. A plane wave is incident from the bottom and all points oscillate in phase inside the slit. To arrive at a distant screen perpendicular to the direction of propagation of the rays, the rays coming from different points inside the slit have to travel different distances. However, the slits are usually closer in diffraction gratings than in double slits, producing fewer maxima at larger angles.
In Figure 5, we see a diffraction grating showing light rays from each slit traveling in the same direction. Each ray travels a different distance to reach a common point on a screen not shown. Where are diffraction gratings used? Diffraction gratings are key components of monochromators used, for example, in optical imaging of particular wavelengths from biological or medical samples. A diffraction grating can be chosen to specifically analyze a wavelength emitted by molecules in diseased cells in a biopsy sample or to help excite strategic molecules in the sample with a selected frequency of light.
Another vital use is in optical fiber technologies where fibers are designed to provide optimum performance at specific wavelengths. A range of diffraction gratings are available for selecting specific wavelengths for such use. However, we can still make a good estimate of this spacing by using white light and the rainbow of colors that comes from the interference. Reflect sunlight from a CD onto a wall and use your best judgment of the location of a strongly diffracted color to find the separation d.
Diffraction gratings with 10, lines per centimeter are readily available. Suppose you have one, and you send a beam of white light through it to a screen 2.
Figure 6. The diffraction grating considered in this example produces a rainbow of colors on a screen a distance from the grating. The distances along the screen are measured perpendicular to the x-direction. In other words, the rainbow pattern extends out of the page. Once the angles are found, the distances along the screen can be found using simple trigonometry.
Substituting these values gives. Notice that in both equations, we reported the results of these intermediate calculations to four significant figures to use with the calculation in Part 2. The distances on the screen are labeled y V and y R in Figure 6. The large distance between the red and violet ends of the rainbow produced from the white light indicates the potential this diffraction grating has as a spectroscopic tool.
The more it can spread out the wavelengths greater dispersion , the more detail can be seen in a spectrum. This depends on the quality of the diffraction grating—it must be very precisely made in addition to having closely spaced lines.
A diffraction grating is a large collection of evenly spaced parallel slits that produces an interference pattern similar to but sharper than that of a double slit. The number of slits in this diffraction grating is too large.
Etching in integrated circuits can be done to a resolution of 50 nm, so slit separations of nm are at the limit of what we can do today. This line spacing is too small to produce diffraction of light. Skip to main content. Wave Optics. Search for:. Multiple Slit Diffraction Learning Objectives By the end of this section, you will be able to: Discuss the pattern obtained from diffraction grating.
Explain diffraction grating effects. Figure 5. Example 1. Calculating Typical Diffraction Grating Effects Diffraction gratings with 10, lines per centimeter are readily available.
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