Diffraction and Interference. 6.1 Diffraction. Diffraction grating. Diffraction grating. Question. Use of a diffraction grating in a spectrometer

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1 irction nd Intererence 6.1 irction irction grting Circulr dirction irction nd intererence re similr phenomen. Intererence is the eect o superposition o 2 coherent wves. irction is the superposition o mny coherent wves. irction grting Consists o lt brrier which contins mny prllel slits seprted by short distnce d. A prllel monochromtic light bem pssing through the grting is dircted by n ngle dsin=m similr to two slit intererence. However, the intensity o the dircted light is higher nd the peks re much nrrower. d irction grting dsin=m two slit intererence multi-slit intererence irction grting m=2 m=1 m=0 m=-1 m=-2 m=2 m=1 m=0 m=-1 m=-2 Use o dirction grting in spectrometer ispersion o light o dierent wvelengths Question A grting in spectrometer hs length o 2 cm nd hs contins 10 4 lines. Find the irst order dirction ngle or light with wvelength o 500 nm. irst order m=1 2 L=2.0 cm L 2x10 m 6 4 2x10 d = = = m N 10 dsin=m N =10 4 slits m 500x10 sin= = = d 2x10 =14.5 o 1

2 Opticl compct disc 10-6 m The closely spced dots ct like dirction grting. brrier point sources For single slit dirction the complex behvior o the wve s unction o the perture is explined by intererence between multiple coherent point sources in the slit. Two Limiting Cses Brrier Ry picture >> Light moves in stright line slit open Lser screen intensity Wve picture << Light spreds out when pssed through smll perture. Wht hppens to the lser bem s the slit decreses? Wht hppens to the light or the generl cse? The pttern spreds out s the slit becomes nrrower slit nrrow Wht hppens to the lser bem s the slit decreses? screen intensity pttern How do we ccount or the im nd mxim? pttern Anlyze ssug Frunhoer dirction conditions. ) Screen r rom the slit or b) Converging lens with screen t the ocl length 2

3 Huygens principle Ech point in the wve in the slit cts s source o sphericl wves. Slit width sum the wves with dierent phses sum mplitude() Find the ngle t the irst imum mplitude = 0 ivide the slit into 2 hlves Light rom every point in the top hl intereres destructively with light rom point in the bottom hl when sin 2 2 drk = sin drk = drk Condition or imum sin drk =m m=+ 1, + 2,... Circulr dirction drk Wves pssing through circulr hole orms circulr dirction pttern. Circulr dirction. Circulr dirction limits the imum size do the spot tht cn be ormed by lens. Circulr hole dimeter The irst imum occurs t = 1.22 According to ry optics. prllel rys rom point t ininity Cn ocus on point t the ocl point o the lens Circulr dirction pttern 3

4 Circulr dirction limits the imum size do the spot tht cn be ormed by lens. According to wve optics. dimeter prllel rys rom point t ininity hs dirction pttern with width o Exmple A cmer lens with n - number (/) equl to 1.4 is used to ocus light rom distnt source. Wht is the dirction limited rdius o the spot tht cn be ormed or 500 nm light? = 1.22 r = (1.22 ) r = = = = (1.22)(500x10 )(1.4) 8.5x10 m 850 nm Close to the wvelength o light r Opticl C ocused lser bem Blu-ry isc 10-6 m The mount o inormtion tht cn be encoded is limited by the dimeter o the dirction-limited spot. Higher density o spot cn be obtined using blue lser with shorter wvelength becuse o the smller size o the dirction limited spot. irction limits the resolution o light microscopes (200 nm) Resolution o two imges by lens just not The resolution o imges is limited by the dirction pttern. 4

5 Ryleigh criterion For resolution o two object by circulr lens o dimeter the dirction limit o resolution occurs when the imge o the second object is t position o the irst imum o the dirction pttern o the irst object. = 1.22 GeoEye 1 Imging Stellite 1.1 m dimeter mirror Resolution 0.41 m Altitude o 684 km irction limit (=550nm) y y = = 1.22 L L 1.22(550x10 m)(684x10 m) y = = = 0.41m 1.1m L Stellite picture o Se World Resolution limit o the eye 2 n=1.00 n eye The eye diers rom simple lens in ir. 1. The light rom the lens trvels through rerctive medi. 2. The light pssing through the middle o the lens chnges direction due to rerction. 3. These two eects cncel so the Ryleigh criterion is the sme s or lens in ir = Resolution limit o the eye Two light sources (= 500nm) re seprted verticlly by 2.0 mm. How r wy cn these objects be by the eye Assume dimeter o the pupil o 2.0 mm. n eye =1.33 y L =2.0 mm 2 wter 2 = 1.22 = 1.22 n wter y = neye 2 = n eye(1.22 ) = 1.22 = nwter L 3 3 y (2x10 )(2x10 ) L = = = 6.6m (500x10 ) irction limit irction limits the resolution o objects viewed through n opticl system Resolution depends on the size o the perture nd the wvelegth o light. Consequences toms cnnot be seen with light microscope (shorter wvelengths re required) Stellite cmers hve limited resolution. To ttin higher resolution. Lrger dimeter lenses Shorter wvelengths. 5