Light Interference Continued…

Constructive Interference Superposition Constructive Interference t +1 -1 + t +1 -1 In Phase t +2 -2 5

Destructive Interference Superposition Destructive Interference +1 t -1 + +1 Out of Phase 180 degrees t -1 t +2 -2 7

Superposition + Different f 1) Constructive 2) Destructive 3) Neither 10

Interference Requirements Need two (or more) waves Must have same frequency Must be coherent (i.e. waves must have definite phase relation) 12

Interference for Sound … For example, a pair of speakers, driven in phase, producing a tone of a single f and l: hmmm… I’m just far enough away that l2-l1=l/2, and I hear no sound at all! l1 l2 Demo 440 Sound Interference But this won’t work for light--can’t get coherent sources 15

Observe Laser Light Through… One Slit: Two Slits: Multiple Slits:

Observe Laser Light Through… One Slit: Broad Central Maximum… Two Slits: Central Bright Spot with symmetric dark fringes. Multiple Slits: Central Bright Spot. Narrowor bright spots, brighter maximums, darker minimums.

Single Slit Diffraction

Double Slit Interference Only Interference + Diffraction

Five Slit Diffraction Grating (Inteference & Diffraction)

How do we predict the locations of the bright and dark fringes produced by a single slit? double slit? Multiple slit?

Young’s Double Slit #1 Light waves from a single source travel through 2 slits before meeting on a screen. The interference will be: Constructive Destructive Depends on L d The rays start in phase, and travel the same distance, so they will arrive in phase. Single source of monochromatic light  L 2 slits-separated by d Screen a distance L from slits 23

Young Double Slit #2 The experiment is modified so that one of the waves has its phase shifted by ½ l. Now, the interference will be: Constructive Destructive Depends on L ½ l shift d The rays start out of phase, and travel the same distance, so they will arrive out of phase. 60% got this correct Single source of monochromatic light  L 2 slits-separated by d Screen a distance L from slits 25

Young’s Double Slit Concept At points where the difference in path length is 0, l,2l, …, the screen is bright. (constructive) 2 slits-separated by d d At points where the difference in path length is the screen is dark. (destructive) Demo 162 2 slit Single source of monochromatic light  L Screen a distance L from slits 27

Young’s Double Slit Key Idea Two rays travel almost exactly the same distance. (screen must be very far away: L >> d) Bottom ray travels a little further. Key for interference is this small extra distance. 30

Young’s Double Slit Quantitative Path length difference = d sin q Constructive interference where m = 0, or 1, or 2, ... Destructive interference Need l < d 32

Young’s Double Slit Quantitative A little geometry… sin(q)  tan(q) = y/L Constructive interference Destructive interference where m = 0, or 1, or 2, ... 33

Young’s Double Slit #3 y d When this Young’s double slit experiment is placed under water. The separation y between minima and maxima 1) increases 2) same 3) decreases Under water l decreases so y decreases 35

Double Slit #4 d Path length difference = d sinq d 1) 2) 1) where m = 0, or 1, or 2, ... Which condition gives destructive interference? d sin() 8

Multiple Slits: (Diffraction Grating – N slits with spacing d) 1 2 4 3 d d Path length difference 1-2 = d sinq =l d Path length difference 1-3 = 2d sinq =2l Path length difference 1-4 = 3d sinq =3l Constructive interference for all paths when 13

Diffraction Grating N slits with spacing d q * screen VERY far away Constructive Interference Maxima are at: Same as for Young’s Double Slit !

Three slit interference 9I0 19

Multiple Slit Interference (Diffraction Grating) Peak location depends on wavelength! For many slits, maxima are still at Region between maxima gets suppressed more and more as no. of slits increases – bright fringes become narrower and brighter. 2 slits (N=2) intensity l 2l 10 slits (N=10) intensity l 2l 22

Single Slit Interference?!

Diffraction Rays This is not what is actually seen! Wall shadow bright Screen with opening (or obstacle without screen) 26

Diffraction/ Huygens Every point on a wave front acts as a source of tiny wavelets that move forward. • Light waves originating at different points within opening travel different distances to wall, and can interfere! demo 1214: metal ruler and green laser pointer • We will see maxima and minima on the wall. 30

Central maximum 1st minima

Single Slit Diffraction 1 1 2 2 W When rays 1 and 1 interfere destructively. Rays 2 and 2 also start W/2 apart and have the same path length difference. Under this condition, every ray originating in top half of slit interferes destructively with the corresponding ray originating in bottom half. 1st minimum at sin q = l/w 33

Single Slit Diffraction 2 2 1 1 w When rays 1 and 1 will interfere destructively. Rays 2 and 2 also start w/4 apart and have the same path length difference. Under this condition, every ray originating in top quarter of slit interferes destructively with the corresponding ray originating in second quarter. 2nd minimum at sin q = 2l/w 35

Single Slit Diffraction Summary Condition for halves of slit to destructively interfere Condition for quarters of slit to destructively interfere Condition for sixths of slit to destructively interfere (m=1, 2, 3, …) All together… THIS FORMULA LOCATES MINIMA!! Narrower slit => broader pattern Note: interference only occurs when w > l l 38

Recap. Interference: Coherent waves Multiple Slits Full wavelength difference = Constructive ½ wavelength difference = Destructive Multiple Slits Constructive d sin(q) = m l (m=1,2,3…) Destructive d sin(q) = (m + 1/2) l 2 slit only More slits = brighter max, darker mins Huygens’ Principle: Each point on wave front acts as coherent source and can interfere. Single Slit: Destructive: w sin(q) = m l (m=1,2,3…) Resolution: Max from 1 at Min from 2 opposite! 50