Thin Film Interference Interference + Light

Superposition t +1 t +1 t Destructive Interference Out of Phase 180 degrees

Superposition t +1 t +1 t Constructive Interference In Phase

Electromagnetic Waves Light, Radio, TV, Microwaves, Satellites, X-Rays

Electromagnetic Waves x z y Transverse (vs. sound waves – longitudinal) E perpendicular to B and always in phase E & B increase and decrease at same times Can travel in empty space (sound waves can’t!) “Speed of light”: v = c = 3 x 10 8 m/s(186,000 miles/second!) Frequency: f = v/  = c/  Period: T = 1/f wave travels one wavelength  in one period T

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

Why should I care about the Index of Refraction? 1.Speed changes when moving to a new medium. 2.Frequency of the light remains constant. 3.Therefore, the wavelength changes. v old  f *  old and v new  f *  new v new / v old  new  old n old / n new = new  old

Thin Film Interference n 1 (thin film) n2n2 n 0 =1.0 (air) t 1 2 Get two waves by reflection off two different interfaces. Ray 2 travels approximately 2t further than ray 1. 37

Reflection + Phase Shifts n1n1 n2n2 Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. If n 1 > n 2 - no phase change upon reflection. If n 1 < n 2 - phase change of 180º upon reflection. (equivalent to the wave shifting by /2.) Incident wave Reflected wave 39

Thin Film Summary n 1 (thin film) n2n2 n = 1.0 (air) t 1 2 Ray 1:  1 = 0 or ½ Determine  number of extra wavelengths for each ray. If |(  2 –  1 )| = ½, 1 ½, 2 ½ …. (m + ½) destructive If |(  2 –  1 )| = 0, 1, 2, 3 …. (m) constructive Note: this is wavelength in film! ( film = o /n 1 ) t/ film ReflectionDistance Ray 2:  2 = 0 or ½ + 0 This is important!

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

Thin Film Practice n glass = 1.5 n water = 1.3 n = 1.0 (air) t 1 2  1 = ½  2 = 0 + 2t / glass = 2t n glass / 0 = (2)(167)(1.5)/500) =1 Blue light (  = 500 nm) incident on a glass (n glass = 1.5) cover slip (t = 167 nm) floating on top of water (n water = 1.3). Is the interference constructive or destructive or neither? Phase shift =  2 –  1 = ½ wavelength 45 Reflection at air-film interface only

Thin Film n glass =1.5 n plastic =1.8 n=1 (air) t 1 2  1 = ½  2 = ½ + 2t / glass = ½ + 2t n glass / 0 = ½ + 1 Blue light = 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 Phase shift =  2 –  1 = 1 wavelength 48 Reflection at both interfaces!

The gas looks: bright dark A thin film of gasoline (n gas =1.20) and a thin film of oil (n oil =1.45) are floating on water (n water =1.33). When the thickness of the two films is exactly one wavelength… t = n water =1.3 n gas =1.20 n air =1.0 n oil =1.45  1,gas = ½ The oil looks: bright dark  2,gas = ½ + 2  1,oil = ½  2,oil = 2 |  2,gas –  1,gas | = 2 |  2,oil –  1,oil | = 3/2 constructivedestructive 50