9.5 Young s Double-Slit Experiment

Transcription

1 9.5 Youg s Double-Slit Experiet Physics Tool box Early attepts to deostrate the iterferece of light were usuccessful because the two sources were too far apart ad out of phase, ad the wavelegth of light is very sall. Thoas Youg s crucial cotributio cosisted of usig oe source illuiatig two closely spaced opeigs i a opaque scree, thus usig diffractio to create two sources of light close together ad i phase. I Youg s experiet a series of light ad dark bads, called iterferece friges, was created o a scree, placed i the path of light, i uch the sae way as those created i the ripple tak. x 1 x L 2 d ad L calculated, give ay three of, x, L,, d, ad The relatioship si. d Path differece of costructive sources are related by 1 2 perit ukows to be P S P S Youg s experiet supported the wave theory of light, explaiig all the properties of light except trasissio through a vacuu. To see the iterferece effects o light, we ust create coditios that allow for us to view soethig too sall for the hua eye to see. To do this we ust create opeigs through which light passes that are coparable i size to the wavelegth of light. If light passes through a large hole, it produced a bright spot o the wall. Now if you ake the hole saller, you still see a bright spot, but you start to see a series of cocetric circles of light appear. This of cause is the diffractio patter. Now if tow sall holes are used you would observe the costructive ad destructive patters (siilar to those observed i a ripple tak) lies are destructive iterferece, lies are costructive iterferece

2 Youg chose the Su as the sae icadescet body, thus the beas of light were always i phases, ad a fixed iterferece patter could be created. We label these bads of bright ad dark as iterferece friges or axia ad iia. This experiet provides very strog evidece for the wave theory of light. The followig figures shows light waves, i phase, eergig fro slits S1 ad S 2, a distace d apart. Although the waves spread out i all directios, we will aalyze the as we ove fro the cetre of the scree or specifically for oly three differece agles. Whe 0 we have both waves reachig the cetre of the scree i phase, also sice the are travellig the sae distace the costructig iterferece occurs, producig a bright spot at the cetre of the scree. Whe the waves fro the secod slit, S2 travel a extra distace of half a wavelegth,, the waves arrive at the scree radias (180) out of phase. Thus destructive 2 iterferece occurs, ad the scree is dark i this regio (this locatio is whe odal lie =1)

3 As we still ove further fro the cetre of the scree, we will reach a poit where the path differece is a sigle wavelegth. Thus the sources are back i phases ad costructive iterferece occurs, causig this regio to be bright. By applyig algebra we discover for destructive iterferece for slit separatio of d The forula; 1 si, 1,2,3,... 2 d By applyig algebra we discover for costructive iterferece for slit separatio of d The forula; si, 0,1,2,3,... d Sice it is very difficult to easure L directly, it is better to easure the ratio x The displaceet betwee adjacet odal lies (a lie of destructive iterferece), x x, x x, x x, thus the forula is give by perpedicular distace fro the slits o the scree. x L d, where L is the x, Actually x L ta, but sice L x ta si

4 For costructive iterferece betwee two sources P S1 P S2 path differece =, 0,1, 2,3,...

5 Exaple 6 A oochroatic source of 450 shies o two slits that are apart. Deterie the agle at which the first-order axiu occurs. Whe a scree is 1.0 away fro the iddle of the slits, for far will the first order axiu be fro the cetre lie? Solutio 1: 6 7 1, d 3.010, x L d L x d Solutio 2: d si d 1 1 si si x si x Exaple 5 If oe slit (source of light) is farther tha the other slit to a poit o the scree, ad light of 600 is used, deterie the order uber of the bright spot. Solutio: The bright spot idicates that costructive iterferece is i effect.

6 P S P S 1 2 Exaple P S1 P S You are to deterie the wavelegth of a source whe it is shoe through slits that are 0.10 apart ad the iterferece patter is created o a scree 2.5 away. You easure the distace betwee the first ad seveth cosecutive dark lies to be 9.0 c. what is the wavelegth. Solutio: Now 9.0c x 6 1.5c odal lies = 6x x L d dx L Exaple The third-order dark frige of 631 light is observed at a agle of 14. How Far apart are the slits. Solutio: si 1 2 d 1 2 d si si