textbook sections Physics 1161: Lecture 26 Interference

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

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

Which type of interference results from the superposition of the two waveforms shown? 1.Constructive 2.Destructive 3.Neither + Different f

Which type of interference results from the superposition of the two waveforms shown? 1.Constructive 2.Destructive 3.Neither + Different f

Interference for Light … Can’t produce coherent light from separate sources. (f  Hz) Single source Two different paths Interference possible here Need two waves from single source taking two different paths –Two slits –Reflection (thin films) –Diffraction *

Coherent & Incoherent Light

Double Slit Interference Applets fendt.de/ph14e/doubleslit.htm fendt.de/ph14e/doubleslit.htm

Young’s Double Slit Applet Physics2000/applets/twoslitsa.html

Young’s Double Slit Layout

Interference - Wavelength

Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be: 1.Constructive 2.Destructive 3.It depends on L Screen a distance L from slits Single source of monochromatic light d 2 slits-separated by d L

Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be: 1.Constructive 2.Destructive 3.It depends on L Screen a distance L from slits Single source of monochromatic light d 2 slits-separated by d L The rays start in phase, and travel the same distance, so they will arrive in phase.

Preflight 26.1 Screen a distance L from slits Single source of monochromatic light d 2 slits-separated by d 1)Constructive 2)Destructive 3)Depends on L L ½ shift The experiment is modified so that one of the waves has its phase shifted by ½. Now, the interference will be:

Preflight 26.1 Screen a distance L from slits Single source of monochromatic light d 2 slits-separated by d 1)Constructive 2)Destructive 3)Depends on L The rays start out of phase, and travel the same distance, so they will arrive out of phase. L ½ shift The experiment is modified so that one of the waves has its phase shifted by ½. Now, the interference will be:

Young’s Double Slit Concept Screen a distance L from slits Single source of monochromatic light d 2 slits-separated by d L At points where the difference in path length is 0,,2, …, the screen is bright. (constructive) At points where the difference in path length is the screen is dark. (destructive)

Young’s Double Slit Key Idea L Two rays travel almost exactly the same distance. (screen must be very far away: L >> d) Bottom ray travels a little further. Key for interference is this small extra distance.

d Path length difference = d Young’s Double Slit Quantitative d sin  Constructive interference Destructive interference (Where m = 0, 1, 2, …) sin(θ)  tan(θ) = y/L

d Path length difference = d Young’s Double Slit Quantitative Destructive interference Constructive interference where m = 0, or 1, or 2,... d sin  Need  < d

d Destructive interference Constructive interference where m = 0, or 1, or 2,... Young’s Double Slit Quantitative y sin(  )  tan(  ) = y/L L A little geometry…

d L Preflight 26.3 y When this Young’s double slit experiment is placed under water. The separation y between minima and maxima 1) increases 2) same3) decreases

d L Preflight 26.3 y When this Young’s double slit experiment is placed under water. The separation y between minima and maxima 1)increases 2) same3) decreases …wavelength is shorter under water.

Preflight 26.2 In the Young’s double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light? 1) Yes2) No

Preflight 26.2 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) Yes2) No Need: d sin  = m => sin  = m   d If   d then   d > 1 so sin  > 1 Not possible!

Reflections at Boundaries Free End Reflection No phase change Slow Medium to Fast Medium to Slow Medium Fixed End Reflection 180 o phase change

Newton’s Rings

Iridescence

Soap Film Interference This soap film varies in thickness and produces a rainbow of colors. The top part is so thin it looks black. All colors destructively interfere there.

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

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 If n 1 < n 2 Incident wave Reflected wave

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

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 ) + 2 t/ film ReflectionDistance Ray 2:  2 = 0 or ½ This is important!

Thin Film Practice n glass = 1.5 n water = 1.3 n = 1.0 (air) t 1 2  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? Phase shift =  2 –  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 = 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 Reflection at air-film interface only

Blue light = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: n glass =1.5 n plastic =1.8 n=1 (air) t Constructive 2.Destructive 3.Neither

Blue light = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: n glass =1.5 n plastic =1.8 n=1 (air) t Constructive 2.Destructive 3.Neither  1 = ½  2 = ½ + 2t / glass = ½ + 2t n glass / 0 = ½ + 1 Phase shift =  2 –  1 = 1 wavelength

Preflights 26.4, 26.5 The gas looks: bright 67 % dark 33 % 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 The oil looks: bright 35 % dark 65 %

Preflights 26.4, 26.5 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 constructive destructive