Here m is the diffraction order (or spectral order),which is an integer. Which governs the angular locations of the principal intensity maxima when light of wavelength λ is diffracted from a grating of groove spacing d. These relationships are expressed by the grating equation At all other angles, the Huygens wavelets originating from the groove facets will interfere destructively. The principle of constructive interference dictates that only when this difference equals the wavelength λ of the light, or some integral multiple thereof, will the light from adjacent grooves be in phase (leading to constructive interference). The geometrical path dif-ference between light from adjacent grooves is seen to be d sin α + d sin β. Other sign conventions exist, so care must be taken in calculations to ensure that results are self-consistent.Īnother illustration of grating diffraction, using wavefronts (surfaces of constant phase), is shown in Figure 2-2. For either reflection or transmission gratings, the algebraic signs of two angles differ if they are measured from opposite sides of the grating normal. In both diagrams, the sign convention for angles is shown by the plus and minus symbols located on either side of the grating normal. By convention, angles of incidence and diffraction are measured from the grating normal to the beam. For red light of wavelength 600 nm, this would give a first order diffraction maximum at about 22°. This is in the range of ordinary laboratory diffraction gratings. The nominal track separation on a CD is 1.6 micrometers, corresponding to about 625 tracks per millimeter. The tracks of a compact disc act as a diffraction grating, producing a separation of the colors of white light. The hydrogen gas in a thin glass tube is excited by an electrical discharge and the spectrum can be viewed through the grating. The illustration shows the hydrogen spectrum. It acts as a "super prism", separating the different colors of light much more than the dispersion effect in a prism. The diffraction grating is an immensely useful tool for the separation of the spectral lines associated with atomic transitions. However, angular separation of the maxima is generally much greater because the slit spacing is so small for a diffraction grating. The condition for maximum intensity is the same as that for a double slit. The relative widths of the interference and diffraction patterns depends upon the slit separation and the width of the individual slits, so the pattern will vary based upon those values. The overall grating intensity is given by the product of the intensity expressions for interference and diffraction. The intensities of these peaks are affected by the diffraction envelope which is determined by the width of the single slits making up the grating. There are multiple orders of the peaks associated with the interference of light through the multiple slits. This illustration is qualitative and intended mainly to show the clear separation of the wavelengths of light. Different wavelengths are diffracted at different angles, according to the grating relationship.Ī diffraction grating is the tool of choice for separating the colors in incident light. Orders 1 and 2 are shown to each side of the direct beam. When light of a single wavelength, like the 632.8nm red light from a helium-neon laser at left, strikes a diffraction grating it is diffracted to each side in multiple orders. The peak intensities are also much higher for the grating than for the double slit. The condition for maximum intensity is the same as that for the double slit or multiple slits, but with a large number of slits the intensity maximum is very sharp and narrow, providing the high resolution for spectroscopic applications. A large number of parallel, closely spaced slits constitutes a diffraction grating. This "super prism" aspect of the diffraction grating leads to application for measuring atomic spectra in both laboratory instruments and telescopes. When there is a need to separate light of different wavelengths with high resolution, then a diffraction grating is most often the tool of choice.
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