Physics 102: Lecture 21 Thin Films & Diffraction Gratings Physics 102: Lecture 21, Slie 1
Recall Interference (at least 2 coherent waves) Constructive (full wavelength ifference) Destructive (half wavelength ifference) Light (1 source, but ifferent paths) Young s ouble slit Thin films Multiple slit X-ray iffraction from crystal Diffraction/single slit Last lecture Toay s lecture Physics 102: Lecture 21, Slie 2
Thin Film Interference Light is incient normal to a thin film Note: angles exaggerate for clarity 1 2 n 0 =1.0 (air) t n 1 (thin film) n 2 Get two waves by reflection off two ifferent interfaces: interference! Ray 2 travels approximately 2t further than ray 1. Physics 102: Lecture 20, Slie 3
Reflection & Phase Shifts Upon reflection from a bounary between two transparent materials, the phase of the reflecte light may change. Reflecte Reflecte Incient n 1 Incient n 1 n 2 n 2 Refracte Refracte If n 1 > n 2 no phase change upon reflection Physics 102: Lecture 20, Slie 4 If n 1 < n 2 180º phase change upon reflection This is like the wave went an extra l/2; =1/2
Thin Film Summary Determine, number of extra wavelengths for each ray. t 1 2 n = 1.0 (air) n 1 (thin film) This is important! Physics 102: Lecture 20, Slie 5 Reflection Ray 1: 1 = 0 or ½ Ray 2: 2 = 0 or ½ If 2 1 = 0, 1, 2, 3. (m) constructive If 2 1 = ½, 1 ½, 2 ½. n 2 Distance + 0 + 2 t/ l film Note: this is wavelength in film! (l film = l o /n 1 ) (m + ½) estructive
ACT: Thin Film Practice Blue light (l 0 = 500 nm) incient on a glass (n 1 = 1.5) cover slip (t = 167 nm) floating on top of water (n 2 = 1.3). t 1 2 n = 1.0 (air) n 1 (thin film) n 2 What is 1, the total phase shift for ray 1 A) 1 = 0 B) 1 = ½ C) 1 = 1 Physics 102: Lecture 20, Slie 6
Thin Film Practice Blue light (l 0 = 500 nm) incient on a glass (n 1 = 1.5) cover slip (t = 167 nm) floating on top of water (n 2 = 1.3). 1 2 n = 1.0 (air) t n 1 (thin film) n 2 Is the interference constructive or estructive or neither? 1 = ½ 2 = 0 + 2t / l glass = 2t n glass / l 0 = (2)(167)(1.5)/500) = 1 Physics 102: Lecture 20, Slie 7 Phase shift = 2 1 = ½ wavelength
ACT: Thin Film Practice II Blue light (l 0 = 500 nm) incient on a glass (n 1 = 1.5) cover slip (t = 167 nm) floating on top of plastic (n 2 = 1.8). t 1 2 n = 1.0 (air) n 1 (thin film) n 2 Is the interference : A) constructive B) estructive C) neither? 1 = 2 = Physics 102: Lecture 20, Slie 8 Phase shift = 2 1 =
Thin film application: Anti-reflection coatings Physics 102: Lecture 20, Slie 9
Diffraction Gratings: multiple slits (N slits with spacing ) Assume screen is very far away (L>>): L θ 1 2 3 4 θ Path length ifference 1-2 = sinq Path length ifference 1-3 = 2 sinq Path length ifference 1-4 = 3 sinq =l =2l =3l Physics 102: Lecture 21, Slie 10 Constructive interference for all paths when sin(q) = ml m = 0, 1, 2
Multiple Slits: (Diffraction Grating N slits with spacing ) Assume screen is very far away (L>>): L θ 1 2 3 4 θ Constructive: sin(q) = ml Hols for arbitrary N m = 0, 1, 2 Same conition as Young s ouble slit! Physics 102: Lecture 21, Slie 11
Checkpoint 2 L θ 1 2 3 θ All 3 rays are interfering constructively at the point shown. If the intensity from ray 1 is I 0, what is the combine intensity of all 3 rays? 1) I 0 2) 3 I 0 3) 9 I 0 Physics 102: Lecture 21, Slie 12
ACT/Checkpoint 3 L θ 1 2 3 θ sin θ = λ 2 When rays 1 an 2 are interfering estructively, is the intensity from the three rays a minimum? A) Yes B) No Physics 102: Lecture 21, Slie 13
intensity intensity Multiple Slit Interference (Diffraction Grating) For many slits, maxima are still at sin θ = m λ Peak location epens on wavelength! Region between maxima gets suppresse more an more as no. of slits increases bright fringes become narrower an brighter. 2 slits (N=2) 10 slits (N=10) 0 l Physics 102: Lecture 21, Slie 14 2l sin(θ) 0 l 2l sin(θ)
Diffraction grating: spreas out ifferent wavelengths, etermine spectrum Solar spectrum! Physics 102: Lecture 21, Slie 15
X-Ray Diffraction: A technique to stuy crystal structure θ θ sin(θ) Crystal soli such as soium Constructive interference: 2 sin(θ) = mλ 0.5nm in NaCl For l=0.017nm X-ray Physics 102: Lecture 21, Slie 16 1 st maximum will be at 10 0 Measure q, etermine
Physics 102: Lecture 21, Slie 17
Single slit interference? Monochromatic light travels through a screen with opening Shaow Bright spot This is not what is actually seen! Physics 102: Lecture 21, Slie 18
Diffraction/Huygens principle Huygens: Every point on a wave front acts as a source of tiny wavelets that move forwar. Light waves originating at ifferent points within opening travel ifferent istances to wall, an can interfere! Physics 102: Lecture 21, Slie 19 We will see maxima an minima on the wall!
Central maximum 1 st minima Next lecture: quantitative single-slit iffraction Physics 102: Lecture 21, Slie 20
Recap Interference: Coherent waves Full wavelength ifference = Constructive ½ wavelength ifference = Destructive Multiple Slits Constructive sin(q) = m l (m=1,2,3 ) Destructive sin(q) = (m + 1/2) l 2 slit only More slits = brighter max, arker mins Single Slit Interference Physics 102: Lecture 21, Slie 21