2 Recall Interference (at least 2 coherent waves) Constructive (full wavelength difference)Destructive (½ wavelength difference)Light (1 source, but different paths)Thin FilmsDouble/multiple slitDiffraction/single slit (today)
3 Young’s Double Slit Review Path length difference= d sinq1)where m = 0, or 1, or 2, ...Which condition gives destructive interference?2)
4 Multiple Slits (Diffraction Grating – N slits with spacing d) 1243ddPath length difference 1-2= d sinq=ldPath length difference 1-3= 2d sinq=2lPath length difference 1-4= 3d sinq=3lConstructive interference for all paths when…
5 Multiple Slits (Diffraction Grating – N slits with spacing d) 1243ddPath length difference 1-2= d sinq=ldPath length difference 1-3= 2d sinq=2lPath length difference 1-4= 3d sinq=3lConstructive interference for all paths when
7 Multiple Slit Interference (Diffraction Grating) Peak location depends on wavelength!For many slits, maxima are still atRegion between maxima gets suppressed more and more as no. of slits increases – bright fringes become narrower and brighter.2 slits (N=2)intensityl2l10 slits (N=10)intensityl2l
8 Same as for Young’s Double Slit ! Diffraction GratingN slits with spacing dq* screen VERY far awayConstructive Interference Maxima are at:Same as for Young’s Double Slit !
9 Diffraction/ HuygensEvery 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!•We will see maxima and minima on the wall.
11 Single Slit Diffraction 1122WWhen rays 1 and 1interfere 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
12 Single Slit Diffraction 2211wWhen rays 1 and 1will 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
13 Single Slit Diffraction Summary Condition for halves of slit to destructively interfereCondition for quarters of slit to destructively interfereCondition for sixths of slit to destructively interfere(m=1, 2, 3, …)All together…THIS FORMULA LOCATES MINIMA!!Preflight 21.3Narrower slit => broader patternNote: interference only occurs when w > l
14 Diffraction from Circular Aperture Central maximum1st diffraction minimumqDiameter DlightMaxima and minima will be a series of bright and dark rings on screenFirst diffraction minimum is atPhysics 1161: Lecture 21, Slide14
15 Intensity from Circular Aperture First diffraction minimaPhysics 1161: Lecture 21, Slide15
16 These objects are just resolved Two objects are just resolved when the maximum of one is at the minimum of the other.
17 Resolving Power To see two objects distinctly, need qobjects » qmin qobjects is angle between objects and aperture:qmintan qobjects d/yqmin is minimum angular separation that aperture can resolve:Dsin qmin qmin = 1.22 l/DydImprove resolution by increasing qobjects or decreasing qmin
18 Recap. Interference: Coherent waves Multiple Slits Full wavelength difference = Constructive½ wavelength difference = DestructiveMultiple SlitsConstructive d sin(q) = m l (m=1,2,3…)Destructive d sin(q) = (m + 1/2) l 2 slit onlyMore slits = brighter max, darker minsHuygens’ 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 2opposite!