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class21lecturenotes

class21lecturenotes - Class 21 Monday March 1 2010 Reading...

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Class 21, Monday, March 1, 2010 Reading: 32. J (mIl.JJ %t<M/:)~' ¥) + "t'r (,R..,~VJijJ fiwd ) Review from last class: - ~i~ dH ~ /~ ~ t:h clJuJ6 J1&r f'~PI~.' I~ "1;" ~/ii tf-'1~) 1/~v'k~ ~ "/let.. ""1- I::. ~ I;, tV' t4t ~r ~ A b"'j4f fo'~ .. /tCIUVU ~14: 7J-L 1: Ii p./ th auP r f a. ~ /riMy.J ~r~ Jln_-{.ln-f-')~ l.- 01 - /)'Ii~cA';fA yd./U)f: ;Y ;W;.f/~ /,r /U{h1A c> d::; " t:tJIau,,~ <. t'.:Jvw~'v~ ~ ... h·,=", _ /1M_Ii J /t.L C l /J tt, 11'''''' in;,! k. J.Y-~~ AM :; 121-1 =:.:.,c:- ~ VI<. e!. / /I :' &, I, IJ ••• o - ~:rItM1.a UtA· I(,IU/« ~fM ~r ,ft 1 - I} " f4 £n;M f{My'l!" ~ l t.u 8". (1,&, /,l, '''' E /tJAK/jMM.MA ~t/~ (uabr t/ j/ljv'" /vI,,?)- I/I.IlIV:;' II· Io / ~'" 1/11 ~h .::. (.2n+I)..l- \ L d Rt,7i.u (JI 'f 1\ .: f tau tJ i'L !r/vlj-0 flye £yrf41 r '" (AM ~ til'" & - .d// ~ ~f ~D it nl,l?fArlr /(MJfI"IP CJtvu,ini./,~i1) 21, I
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We ended last class with an example and the following question: Given two experimental setups, one involving a double·slit and one involving a diffraction grating, which one will have a better resolution of two very close wavelengths? We picked the Sodium doublet, "'1=589 nm and '-z=589.6 nm. What does resolution mean? How far apart are two bright fringes of a given order, n. on the screen? Are they even separated well enough so that they can be seen as two distinct bright lines? Double-Slit Ojffraction Grating ~= ~ ~11. I/h Un ~ /J j ~ ~n: ~ft«.( /l·t) r/::: ~ :) t7n ~ a~ul'tt{ n-fl~) Ph -= ",utt-W (n·;";';\,) =) $In, ~ L ~ tin/ Py n -::. I L=lm J /=(J.YUtfl./: .I I /Jill. ... ~YC~(n.I'f.AL) 1:) Yn~:: ~tfhz. 'ft.;; - 'In = / IJf' /J. 6' ./p-f/tt j J foi' II:: I~&{) ./tUtA / ItUM.. 4. n:. / p.ft'/U ~ =) t1, = MC,;w' (ICJtJ O . JI7'1()-~::: I lo-J(,tA. :: atC.ftk( p.rl'!) :::J(.ol{# ~ • / ItXJ Q J/'l 6 -It) -7/,A.{ )::. 2. e a rcSiM C/~ -11M. . o :: arcSMA (tJ.rJ9().: i/.12/ = ') £J,: 11M· tit,u (lb. oK;: (). 111/ m.. Vz..;: 1'J14' ~ (J(: 121''1 = (). ;.l19( Ut... .-:.) 1z-'/, = 1.16·/0 -JIM, [lIb;Ul1M. J ;; S1 tkf/')vt : Tiu tit/lrlfcA"lC<. 7aA~ ~rtlle6J Il~ t~ t/oul:l ~a~'" In"j6f Piw> - _ ~ 'dtil" It. a<-t. a;, 11',;<44 ~t' / Itt 1,,1,1, /J .; t( ft..t IAI. )(1", 4 _L ~rA 6;?'~:Fir %tf ¥"--A7; Ii cdLt,t. dt{~~rfl(}YI... I" a,vJ4 /-- 2 ftf,l J/ly d . j,/Ad 15 //w /t1U~11 for tIu-y /;dftr f'n'~; . ll, 2.
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One most useful application of the diffraction grating is the spectroscope, which you have used on numerous occasions in your chemistry labs to analyze the composition of substances whose atoms or molecules are excited to emit electromagnetic radiation corresponding to the allowed transitions of the electrons within these atoms. For example, in the visible range of the spectrum, Hydrogen gas has four emission lines. When this light is passed through a diffraction grating, at the center of the screen a bright, white-light fringe is formed, as all these colors experience constructive interference there. For all subsequent maxima of interference, the different colored fringes have their distinct location on the screen, as a result of their different wavelengths. As the order, n, increases, these fringes get increasingly more spread out (see figure below). In this example, the red bright fringe corresponding to the fourth order, n=4, no longer show up on the screen. Why might that be? ,. vlst v , t r v " i- ] - , I ~ - II \, I I , 1 , •" I I~ I I.
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