LECTURE 26: Interference

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1 ANNOUNCEMENT *Final: Thursday December 14, 2017, 1 PM 3 PM *Location: Elliot Hall of Music *Covers all readings, lectures, homework from Chapters 28.6 through 33. *The exam will be multiple choice. Be sure to bring your student ID card and a hand-written one-page (two sided) crib sheet plus the original (or revised) crib sheets that you prepared for exams 1 and 2. NOTE THAT FEW EQUATIONS WILL BE GIVEN YOU ARE REMINDED THAT IT IS YOUR RESPONSIBILITY TO CREATE WHATEVER TWO-SIDED CRIB SHEET YOU WANT TO BRING TO THIS EXAM. 11/29/17 The equation sheet that will be given with the exam is posted on the course homepage. Click on the link on the left labeled EquationSheet 1

2 LECTURE 26: Interference ~0.34 µm ~0.15 µm (λ = 780 nm) (λ = 650 nm) BLU-RAY (λ = 405 nm)

3 Interference When two waves with the same frequency f and wavelength λ combine, the resultant is a wave whose amplitude depends on the phase different, δ. 11/29/17 3

4 Interference: Phase Differences Constructive Interference δ = 0 or 1λ Destructive Interference δ = 0.5 λ δ = 0.3 λ 11/29/17 4

5 Coherence *If the difference in phase between two (or more) waves remains constant ( i.e., time-independent), the waves are said to be perfectly coherent. *A single light wave is said to be coherent if any two points along the propagation path maintains a constant phase difference. *Coherence length: the spatial extent over which a light wave remains coherent. Only coherent waves can produce interference! 11/29/17 5

6 Coherence Infinite coherence length Finite coherence length Single Photon 11/29/17 6

7 Intensity of Two Interfering Waves *Two light waves not in phase: 11/29/17 7

8 Intensity of Two Interfering Waves *Maxima occur for: *Minima occur for: for m = 0, 1, 2, 3. 11/29/17 8

9 Interference *Three ways in which the phase difference between two waves can change: 1. By traveling though media of different indexes of refraction 2. By traveling along paths of different lengths 3. By reflection from a boundary 11/29/17 9

10 Interference: Different Indexes of Refraction *The phase difference between two waves can change if the waves travel through different material having different indexes of refraction. n 1 n 2 L 11/29/17 10

11 Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. Thomas Young experiment (1801) Remember Huygen s principle. 11/29/17 11

12 Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. 11/29/17 12

13 Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. 11/29/17 13

14 Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. Spacing between fringes: 11/29/17 14

15 Interference: Reflection from a Boundary *The phase difference between two waves can change if one or both are reflected. Reflection Reflection Phase Shift Off lower index zero Off higher index 0.5λ 11/29/17 15

16 Interference: Soap Bubble *The phase difference between two waves can change if one or both are reflected. DEMO: Soap Bubble mirror light beam projector screen soap film Colored interference fringes will be seen on the screen. 11/29/17 16

17 Interference: Soap Bubble The phase difference between the two waves is caused by: 1. Phase shift on reflection for ray 1 of 0.5 λ. Ray 2 does not phase shift on reflection. Valid for n 2 > n 1 and n 2 > n 3 2. Path length difference between ray 1 & ray 2 is 2t. Ray 2 crosses the film twice. For in-phase waves (maxima - bright fringes): For out of-phase waves (minima - dark fringes): The total difference between ray 1 and ray 2 is the extra difference traveled plus the shift due to reflection. 11/29/17 17

18 Interference of Reflections from a film of water 11/29/17 18

19 Interference of Reflections from a film of water 11/29/17 19

20 Newton s Rings no phase change optical flat ~ zero path length difference phase change 11/29/17 20

21 Coating a Glass Lens to Suppress Reflections: phase change at both a and b since reflection is off a more optically dense medium 2 1 vacuum deposited t 11/29/17 21

22 Coating a Glass Lens to Suppress Reflections: For λ = 550 nm and least thickness m = 0. Note that the thickness needs to be different for different wavelengths. 11/29/17 22