![]() ![]() If the lines are to be narrow, the angular separation δθ is small, then corresponding wavelengths interval Δλ must be small, and by equation(1) the resolving power must be large. Where λ = λ 1 + λ 2 /2 and Δλ = λ 1 – λ 2 Thus, resolving power increases with the increasing order number and with an increasing number of illuminated slits. According to Rayleigh’s Criterion ” For two nearly equal wavelengths λ 1 and λ 2 between which a diffraction grating can just barely distinguish, the resolving power R of the grating is defined as: R = λ/Δλ Thus,a grating that has a high resolving power can distinguish small differences in wavelength. The grating is the more precise device if we want to distinguish two closely spaced wavelengths. Like the prism, the diffraction grating can be used to disperse a spectrum into its wavelength components. The diffraction grating is most useful for measuring accurately. “The resolving power of grating is a measure of how effectively it can separate or resolve two wavelengths in a given order of their spectrum”. “The resolving power of an instrument is its ability to reveal minor details of the object under examination.” Resolving Power of grating Note that the dispersion does not depend on the number of rulings N. We can also increase the dispersion by working at higher-order ( large m). Since the grating equation is: d Sinθ =mλ Differentiating the above equation we have: d cosθdθ = mλ Now in terms of small differences the above equation we have: d cosθ dθ =m dλ Now in terms of small differences, the above relation can be written as: d cosθ Δθ =mΔλ Δθ/Δλ =m/d cosθ D = m/d cosθ From the above relation, we see that the dispersion D increases as the spacing between the slits ‘d’ decreases. The dispersion D of the grating is defined as: “The angular separation Δθ per unit wavelength Δλ is called the dispersion D of the grating.” D = Δθ/Δλ For lines of nearly equal wavelengths to appear as widely as possible,we would like our grating to have the largest possible dispersion. The separation Δθ between the spectral lines that differ in wavelength by small amount Δλ.The ability of a grating to produce spectra that permit precise measurement of wavelengths is determined by two intrinsic properties of grating. Therefore, the condition for maxima in the interference pattern at the angle θ is. If this path difference is equal to one wavelength or some integral multiple of a wavelength, then waves from all slits are in phase at point P and a bright fringe is observed. From the figure, we note that the path difference’ δ ‘ between rays from any two adjacent slits is equal to d sin θ. However, for some arbitrary direction θ measured from the horizontal, the waves must travel different path lengths before reaching point p. The waves from all slits are in phase as they leave the slits. Each slit is produced diffraction, and the diffracted beams interfere with one another to produce the final pattern. The pattern observed on the screen is the result of the combined effects of interference and diffraction. A converging lens brings the rays together at point P. A plane wave is an incident from the left, normal to the plane of the grating. ![]() A section of a diffraction grating is illustrated in the figure. For example, a grating ruled with 5000 lines/cm has a slit spacing d=1/5000 cm=2.00×10 -4 cm. Gratings that have many lines very close to each other can have very small slit spacing. A reflection grating can be made by cutting parallel lines on the surface of refractive material. ![]() The space between the lines is transparent to the light and hence acts as separate slits. A transmission grating can be made by cutting parallel lines on a glass plate with a precision ruling machine. The space between lines acts as slits and these slits diffract the light waves thereby producing a large number of beams that interfere in such a way to produce spectra. It consists of a large number of equally spaced parallel slits.” Its working principle is based on the phenomenon of diffraction. “The diffraction grating is a useful device for analyzing light sources. ![]()
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