Physics 102 Exam 3 Review: Light Interference & Thin Films

1. Hour Exam 3 • Monday, Apr. 18 (two weeks from today!) • Lectures 14 – 21 • Homework through HW 11 • Discussions through Disc 11 • Review session • Sunday, Apr. 17, 3pm, 141 Loomis • Will cover Fall ‘10 exam 3 • Sign up for conflict exam!

2. Physics 102: Lecture 20 Interference

3. Phys 102 recent lectures Light as a wave • Lecture 14 – EM waves • Lecture 15 – Polarization • Lecture 20 & 21 – Interference & diffraction Light as a ray • Lecture 16 – Reflection • Lecture 17 – Spherical mirrors & refraction • Lecture 18 – Refraction & lenses • Lecture 19 – Lenses & your eye

4. +1 t -1 +1 t -1 +2 t -2 Superposition ConstructiveInterference + In Phase

5. +2 t -2 Superposition Destructive Interference +1 t -1 + +1 Out of Phase 180 degrees t -1

6. ACT: Superposition + Different f 1) Constructive 2) Destructive 3) Neither

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

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

9. Interference for Light … • Can’t produce coherent light from separate sources. (f  1014 Hz) • Need two waves from single source taking two different paths • Two slits • Reflection (thin films) • Diffraction* Today’s lecture Next lecture

10. Young’s double slit/rays Monochromatic light travels through 2 slits onto a screen What pattern emerges on the screen? Shadow Bright spots This is not what is actually seen!

11. Young’s double slit/Huygens Recall Huygens’ principle: Every point on a wave front acts as a source of tiny wavelets that move forward. Bright and dark spots on screen! • Constructive = bright • Destructive = dark Wave crests in phase = constructive interference

12. Young’s double slit: Key idea Consider two rays traveling at an angle q: • θ • Bottom ray travels a little further (2l in this case) Key for interference is this small extra distance.

13. Young’s double slit: Quantitative Consider two rays traveling at an angle q Assume screen is very far away (L>>d): ≈ ≈ • θ θ ≈ d • m = +2 Path length difference = dsin(q) L Constructive: dsin(q) = ml Destructive: dsin(q) = (m+1/2)l where m = 0, 1, 2 Need l < d

14. Young’s double slit: Quantitative y Assume screen is very far away (L>>d), angles q are small: m = +2 θ m = +1 θ L d m = 0 dsin(q) sin(q)  tan(q) = y/L m = -1 Constructive: dsin(q) = ml Destructive: dsin(q) = (m+1/2)l y ≈ mlL/d m = -2 y ≈ (m+1/2)lL/d m = 0, 1, 2

15. y ACT: Preflight 20.3 When this Young’s double slit experiment is placed under water, the separation y between minima and maxima: m = +2 θ m = +1 θ d m = 0 L dsin(q) m = -1 m = -2 1) increases 2) same 3) decreases 19% 26% 55% Under water l decreases so y decreases!

16. Need: d sin q = ml => sin q = ml / d Not possible! Preflight 20.2 In the Young double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light? 1) Yes 2) No If l > d then l / d > 1 sosin q > 1

17. 1 2 Thin Film Interference Light is incident normal to a thin film Note: angles exaggerated for clarity n0=1.0 (air) n1 (thin film) t n2 Get two waves by reflection off two different interfaces: interference! Ray 2 travels approximately 2t further than ray 1. Why stop at 2 reflections?

18. Reflection & Phase Shifts Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. Reflected Reflected Incident Incident n1 n1 n2 n2 Refracted Refracted • If n1 > n2 – no phase change upon reflection • If n1 < n2 – 180º phase change upon reflection (shift by l/2)

19. This is important! Reflection Distance Thin Film Summary Determine d, number of extra wavelengths for each ray. 1 2 n = 1.0 (air) n1 (thin film) t n2 Note: this is wavelength in film! (lfilm= lo/n1) Ray 1: d1 = 0 or ½ + 0 Ray 2: d2 = 0 or ½ + 2 t/ lfilm If |d2 – d1| = 0, 1, 2, 3 …. (m) constructive If |d2 – d1| = ½ , 1 ½, 2 ½ …. (m + ½) destructive

20. What is d1, the total phase shift for ray 1 A) d1 = 0 B) d1 = ½ C) d1 = 1 ACT: Thin Film Practice Blue light (l0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of water (n2 = 1.3). 1 2 n = 1.0 (air) n1 (thin film) t n2

21. Example Thin Film Practice Blue light (l0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of water (n2 = 1.3). 1 2 n = 1.0 (air) n1 (thin film) t n2 Is the interference constructiveor destructive or neither? d1 = ½ d2 = 0 + 2t / lglass = 2t nglass/ l0= (2)(167)(1.5)/500) = 1 Phase shift = |d2 – d1| = ½ wavelength

22. Example ACT: Thin Film Practice II Blue light (l0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of plastic (n2 = 1.8). 1 2 n = 1.0 (air) n1 (thin film) t n2 Is the interference : 1) constructive 2) destructive 3) neither? d1 = ½ d2 = ½ + 2t / lglass = ½ + 2t nglass/ l0= (2)(167)(1.5)/500) = 3/2 Phase shift = |d2 – d1| = 1 wavelength

23. See you Wednesday!