PHYS 450 Fall semester Lecture 08: Young s Double Slit. Ron Reifenberger Birck Nanotechnology Center Purdue University

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1 /4/6 PHYS 45 Fall semester 6 Lecture 8: Young s Double Slit Ron Reifenberger Birck Nanotechnolog Center Purdue Universit Lecture 8 Young s Double Slit Experiment 83 ( double path genre of experiments) Is this what happens? Prediction based on ra nature of light

2 /4/6 EXPERIMENT: A sequence of bright and dark fringes are observed on a viewing screen! idth of slit = a Assume a < Interference Pattern Side view! 3 Interference THREE Underling Assumptions Fresnel s work in 87 combines Hugen s principle of wave propagation and Young s ideas about interference x Coherence requirement is readil achieved b a laser ave spreads out after passing through a narrow slit Phase difference between different optical paths and determines intensit at x Conditions that must be satisfied: Monochromatic: Light with a specific wavelength Coherent: Phase difference between light waves arriving at an location remains constant over time 4

3 /4/6 Model to Explain Young s Double Slit Ke Idea: Two coherent light beams interfere after following different paths light source Out of phase b 8 o (or π) Important historicall because it allowed an eas wa to measure the wavelength of light 5 Recent Histor of -Slits in Phsics In 967, two-source interference using TO separate lasers as light sources In 999, the double-slit experiment was demonstrated with Buckball molecules (comprised of 6 carbon atoms, diam=7 nm) In, the double-slit experiment with electrons as described b Richard Fenman was again carried out, this time using two slits of 6 nm wide 4 μm long In 3, the double-slit experiment was successfull performed with molecules that each comprised 8 atoms (whose total mass was over, atomic mass units) 6 3

4 /4/6 Optical Path Length Difference in Young s Double Slit Geometr a) b) Top view! screen screen near screen far screen c) as distance to screen increases, θ θ and is the limiting condition for parallel ras) d two parallel ras OPL= dsin() 7 Constructive interference when optical path length difference is an integer a P m th bright fringe a is amplitude of E-field at point P from top slit slits OPL d if <<, sinθ Θ ae i screen Top view! OPL d sin phase difference : d sin d 8 4

5 /4/6 Intensit at point P i at point P, A a ae dsin d i i i i I A aae aae a a e e a e i i a a a e cos 4 cos a Details, details Locations of maximum Intensit maximum when,,,, m or when,, 4,, m dsin,,4,,m dsin,,4,,m m sin tan d Intensit (au) Two Slits; d=m, =638 nm; =5 m exact approximate (in m) 3 Separation between maxima (approx) m m d m m d m m m m d d d 9 Constructive/Destructive Interference Two Slits OPL is optical path length difference between and is resulting phase difference m= Bright OPL= = Dark OPL=/ = Bright OPL= = m= 5

6 /4/6 BEARE: prior discussion treats a as a constant and ignores dependence of a with width of single slit The observed intensit of fringes from two slits is modulated as increases =l idth of central maximum screen See Appendix for more details Apparatus Young s Two Slit Laser Two Slits Reflecting Mirror 6

7 /4/6 Measurements Set Pattern Slit idth Slit Separation Measure C A 4mm 5mm l B A 4mm 5mm l B C 8mm 5mm width of central max width of central max 965B PASCO OS-965 slit set: Electroformed Ni foil Dimensions in mm Tolerances: 5 mm Slit Space dimension is center-to-center of each slit 3 Extension of Young s Interference: Llod s Mirror (834) 4 7

8 /4/6 Review: Tracking the Phase Upon Reflection Must Include Possible Phase Change upon Reflection KEY IDEA Keep track of the phase!! air n= thin film n air n= Not to scale Reflection off interface from low n to high n: 8 o () phase change Reflection off interface from high n to low n: no phase change 5 Source S (near grazing incidence) d OPL Virtual Source S (smmetric to mirror plane) Llod s Mirror Relevant Geometr phase shift D OPL tan D d ❶ a ❷ ae i (834) Viewing Screen P Front Surface Mirror hen light from two paths are in phase, a bright fringe appears on viewing screen hen light from two paths are out of phase, a dark fringe appears on viewing screen OPL d sin phase difference : d sin d d D 6 8

9 /4/6 Multiple Fringes D Viewing Screen m- Source S (near grazing incidence) Virtual d Source S (smmetric to mirror plane) m- m m+ Front Surface Mirror Grazing Beam m m+ 7 Intensit i d sin Aaae where i i i i I A aae aae a a e e a i i e e a a a cos 4a cos 3 Separation between maxima (approx) Details, details D m m d 3 D m m d 3D D D m m m m d d d Locations of maximum intensit maximum when,,,, m or when,, 4,, m d,,4,,m D d D D,, 4,, d D 3 5,,,, m d D m d The ratio D/d is difficult to measure accuratel,, 4,, m m 8 9

10 /4/6 Apparatus Llod s Mirror Laser Adjustable Vertical Slit path of laser beam Llod s Mirror Llod s Mirror Lens (f~ +5 cm) Reflecting Mirror Lens Reflecting Mirror 9 Procedure: Calibrate D/d using known HeNe laser line NO changes in optical alignment allows wavelength calibration of other HeNe lines Fringes from Llod s Mirror =6 nm ~ inches Lens Imperfections ~7 inches Available HeNe gas lasers: red (638 nm) orange (6 nm) ellow (594 nm) green (543 nm) =63 nm

11 /4/6 Comparison between Young and Llod Young Llod central feature bright dark d, separation between slits basicall fixed adjustable Primar use Measure wavelength of light Produces interference patterns over large areas Up Next Interferometers

12 /4/6 The Intensit through a Single Slit Let b now equal the width of slit b I E tot I=(E +E ) NOT I= E +E i N θ Δ(OPL) i E o E coskrt N Eo Ei coskrti N hat happens when b is comparable to? E o sin OPL i i i 3 In the limit of infinitel man point sources, convert the sum to an integral over position of all points in the slit: Let the center of the slit define = Here, the width of the slit equals b It follows that varies from b/ to b/ For the E-field amplitude we have b E Eo sin sin coskrt bsin For the time averaged intensit we have (ω=π/t =πf) E b b o E E dcos kr t d kr t b b b sin sin E b sin T time o Eo sin cos b b b b Eo sin kr t sin sin kr t sin b sin cos kr t dt T dt 4

13 /4/6 orking it out T E T time o cos b sin sin E b sin cos kr t dt sin T T 4 dt kr t kr t sin kr T kr T sin kr kr T 4 T 4 sin kr kr 4 sin kr kr 4T sin krcos4 kr sin 4 sin kr 4T sin kr4 sin kr 4 T kr t dt dt T b sin sin I E E time o b sin b sin sin I o b sin Note that I is the same as a on slides 9-5 phase= Defining the phase of a wave phase x = x = π λ x x (x) = Asinπ λ x phase x = x = π λ x x Δ = x-x = π -π λ λ x π π x = x -x = Δx πm m = integer λ λ x E E x 6 3

14 /4/6 Ke Idea: Adding in-phase and out-of-phase signals The phase of the sine wave is measured in radians a) x x Asin o π Asin o π Δφ λ λ In Phase SUM The superposition of two waves b) E (N/m) position (m) Out of Phase Δφ =,π, 4π, SUM= E (N/m) - Δφ = π, 3π, position (m) Principle of Superposition 7 Example Monochromatic light of unknown wavelength passes through two narrow slits that are separated b d=5 m A viewing screen is placed m behind the double slits The 4 th bright fringe observed on the screen is located 8 cm from the central bright fringe hat is the wavelength of the light? d dsin θ =mλ constructive λ dsinθ' = m+ λ = m+ destructive where m =,±,±,±3, θ = cm Y=8 cm Viewing screen dsinθ =mλ or d mλ Is <<? -6 8 cm 5 m = 4λ cm -6 5 m 8 cm λ = 4 cm -6 5 =375-7 =565 m=565nm 8 4