Sin θ m = nmλ where m is the order of the fringe. Instead of specifying the interslit spacing d, we normally cite the number of slits per unit length, n. Physics 102 Lab 8: Measuring wavelengths with a diffraction grating. In all cases, if the slit separation is d, the condition for a strong maximum is the same as for Young's experiment, i.e.ĭ sin θ m = mλ where m is the order of the fringe. So let's now look at fringes with large numbers of slits. So, as we increase the number of slits, the width of the fringes becomes narrower, their brightness increases, and the subsidiary maxima are proportionally less important. Remember that the intensity goes as the square of the amplitude, so the intensity of the bright fringes represented in the diagrams above would go as 2 2 : 3 2 : 4 2 = 4 : 9: 16 = 1 : 2.25 : 4. Note also that the height of the maxima increases, because more slits contribute to it. For two slits, the range of φ is 2π = 4π/2 for three slits it is 4π/3, for four slits it is 4π/4 and, for N slits it is 4π/ N. the spacing between the zeros on either side. A diffraction grating is an arrangement consisting of a large number of parallel slits of same width and separated by equal opaque spacing. For four slits, the first zero occurs at φ = π/2 and there are two small subsidiary maxima.Ĭonsider the width of the large maximum, i.e. With three slits having the same spacing, the same varation in θ and thus φ takes us from central maximum, to zero at φ = 2π/3, to a small subsidiary maximum at φ = 2π/2 = π, to zero at φ = 4π/3 and back to a maximum at φ = 2π. With two slits, as φ varies from 0 to 2π, the phasor sum rotates so that its amplitude goes from maximum to zero to maximum. In Diffraction, we saw that the phase difference at angle φ θ between rays from two sources distance a apart was φ = 2π a sin θ/ λ. In each case, the angle between adjacent phasors scans from 0 to 2π. As the angle on the diffraction pattern is varied, the angle between the phasors varies and, at the same time, the black vertical line scans, in synchrony, across the plot of intensity. The distance between the two ends of the figure is the amplitude of the resultant pattern, and the intensity, which is graphed at right, is proportional to the square of the amplitude. In each of the animations below, we see at left the phasor diagram for the appropriate number of sources. To understand the pattern produced by a diffraction grating with many slits, let's begin with Young's experiment (two slits) and add more. The images below show the dispersion patterns made with the same grating for a sodium lamp, a mercury lamp, an incandescent lamp and a candle. The sketch at right shows (top) a light source illuminating a grating, with the dispersed image projected on a distant screen. Patterns with monochromatic and broad band sources.This page supports the multimedia tutorial Diffraction. A grating disperses light of different wavelengths to give, for any wavelength, a narrow fringe. A grating is a set of equally spaced, narrow, parallel sources. Diffraction gratings allow optical spectroscopy.
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