Thin Film Interference

1. Thin Film Interference Interference + Light

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

3. +1 t -1 +1 t -1 +2 t -2 Superposition ConstructiveInterference + In Phase

4. Electromagnetic Waves • Light, Radio, TV, Microwaves, Satellites, X-Rays

5. y x z Electromagnetic Waves • Transverse (vs. sound waves – longitudinal) • E perpendicular to B and always in phaseE & B increase and decrease at same times • Can travel in empty space (sound waves can’t!) • “Speed of light”: v = c = 3 x 108 m/s (186,000 miles/second!) • Frequency:f = v/l = c/l Period: T = 1/f • wave travels one wavelength l in one period T

6. Index of Refraction Speed of light in vacuum Speed of light in medium Index of refraction In general n increases with density of the medium. 186,000 miles/second: it’s not just a good idea, it’s the law! so always!

7. Index of Refraction • Speed changes when moving to a new medium. • Frequency of the light remains constant. • Therefore, the wavelength changes. • vold = f * lold and vnew = f * lnew • vnew / vold= lnew / lold nold/nnew = lnew / lold

8. 1 2 Thin Film Interference n0=1.0 (air) n1 (thin film) t n2 Get two waves by reflection off two different interfaces. Ray 2 travels approximately2t further than ray 1. 37

9. Reflected wave Incident wave n1 n2 Reflection + Phase Shifts Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. • If n1 > n2 - no phase change upon reflection. • If n1 < n2 - phase change of 180º upon reflection. (equivalent to the wave shifting by l/2.) 39

10. This is important! Distance Reflection 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 42

11. What is d1, the total phase shift for ray 1 A) d1 = 0 B) d1 = ½ C) d1 = 1 Example Thin Film Practice 1 2 n = 1.0 (air) nglass = 1.5 t nwater= 1.3 Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither? 45

12. Example Thin Film Practice 1 2 n = 1.0 (air) nglass = 1.5 t nwater= 1.3 Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither? 45

13. Thin Film Blue light l = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: (A) constructive (B) destructive (C) neither 1 2 n=1 (air) nglass =1.5 t nplastic=1.8 48

14. nair=1.0 t =l noil=1.45 ngas=1.20 nwater=1.3 A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength… • The gas looks: • bright • dark • The oil looks: • bright • dark 50

15. Thin Film Practice 1 2 n = 1.0 (air) nglass = 1.5 t nwater= 1.3 Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither? 45

16. Thin Film Practice 1 2 n = 1.0 (air) nglass = 1.5 t nwater= 1.3 Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3). Is the interference constructive or destructive or neither? 45