ics Fri Feb.02. Announcements Diffrction Difrrction Grtings Fridy, Februry 2, 2007 Help sessions: W 9-10 pm in NSC 118 Msteringics WU #5 due Mondy WU #6 due Wednesdy http://www.voltnet.com/ldder/ A bem of light of wvelength 580 nm psses through two closely spced glss pltes s shown. Wht is the minimum plte seprtion d > 0 for which the trnsmitted light be mximlly bright? Seprte Worksheet Worksheet Problem #1 d 1 2 1) 145 nm 2) 290 nm 3) 435 nm 4) 580 nm 5) 725 nm 6) 1160 nm 7) Cnnot determine In studying the two slit interference pttern, we ve mde some simplifying ssumptions nd neglected some importnt physicl processes. Perhps the most importnt of these is clled The wy we ve drwn our digrms for the 2-slit interference, we ve included the process lredy without relly commenting on its existence. et s tke close-up view of one of the slits... 1
If light is trvelling in stright pth, why don t we observe the following: Geometric optics cnnot explin the diffrction-- the bending of light round edges--tht is ctully observed in our experiments with the slits) When we project the light pssing through single slit onto distnt, guess wht we see Centrl mximum Secondry mxim Right bout this point, you should be sking yourself... 2 1 1 2 Why in the world should light from single slit produce wht looks like n interference pttern on the???? Secondry minim It is useful to employ Huygens principle to try to explin our observtions... Huygens principle dvises us to tret ech portion of wve front of light s source of light wves... A drk spot will pper on the t loctions where the pth length difference,, is hlf wvelength. Thinking bout the problem this wy llows us to see the single slit s contining lrge number of sources, ech of which cn interfere. = 2 sin = 2 minim 2
This is true for ny pir of sources seprted by hlf the slit width... Destructive interference will occur s long s the pth length difference is some integer multiple of the quntity / Therefore, ngles t which destructive interference occurs re given by sin = m = 2 sin = 2 minim Where m = +/- 1, +/- 2, +/- 3,. As with the two-slit interference pttern, we cn relte the distnce bove the centrl mximum of ech drk fringe with little geometry... y sin tn = = m y Notice tht when the slit width,, is less thn the wvelength, the quntity on the right side is greter thn 1! y sin tn = = m Therefore, for <, we will not observe the diffrction interference pttern. The secondry mxim cn be found on either side of the centrl mximum pproximtely hlf-wy between the loctions of successive minim. The centrl mximum is found t the ngle = 0. The secondry mxim pper t ngles given by: y 1 sin tn = = ( m + ) 2 Note tht the centrl mximum is twice s wide s the secondry mxim. The formule for the diffrction pttern look lot like those we sw for the two-slit interference pttern, but they re very different! Two-slit mxim sin = m d Diffrction minim sin = m 3
A bem of green light is diffrcted by slit of width 0.550 mm. The diffrction pttern forms on 2.06 m wy from the slit. The distnce between the zero intensity res on both sides of the centrl mximum is 4.10 mm. Wht is the wvelength of the lser light? Worksheet Problem #2 1) 274 nm 4) 15 nm 2) 547 nm 3) 821 nm 5) 2189 nm 6) Cnnot determine Conceptully, it s quite simple to extend our discussion of diffrction nd Young s experiment to the cse of the interference pttern produced from n object known s Insted of the lrge number of sources tht we considered in the diffrction pttern using Huygen s principle, the diffrction grting consists of very lrge number of slits, ech one of which cts s its own source. Diffrction Grting Diffrction Grting N slits N slits You cn think of it s n N-slit interference pttern (where N is the number of slits). Diffrction grtings re usully described by the number of slits per unit length. As in Young s experiment, the observed diffrction pttern depends upon the slit seprtion, the wvelength of the incident light, nd the ngle to the. observed interference pttern N-slit mxim sin = m d Where m is the order number nd d the slit seprtion, given by / N for the diffrction grting. Notice tht these lines tend to be very nrrow. -2-1 0 1 2 centrl mximum Order of the Secondry mxim We cn proceed s before (using geometry) to locte the mxim. As you will see in the lbortory, diffrction grtings provide gret wy to seprte the constituent wvelengths of incident light, since ech wvelength will hve unique ngle for the ppernce of bright lines when exmined through the grting. All wvelengths will hve bright t ngle = 0, so bright white line usully ppers t this ngle. 4
ight from n rgon lser strikes diffrction grting with 5310 lines per centimeter. The centrl nd 1 st order principl mxim re seprted by 0.488 m on wll 1.72 m from the grting. Wht is the wvelength of the lser light? Worksheet Problem #4 Worksheet Problem #3 1) 257 nm 2) 514 nm 3) 534 nm 4) 1028 nm 5) 1068 nm 6) impossible to determine 5