Physics 1161 Lecture 26 Interference textbook sections 28

Physics 1161: Lecture 26 Interference • textbook sections 28 -1 -- 28 -3

Superposition Constructive Interference +1 t -1 + +1 In Phase t -1 +2 t -2

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

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 1014 Hz) • Need two waves from single source taking two different paths – Two slits – Reflection (thin films) – Diffraction* Two different paths Interference possible here Single source

Coherent & Incoherent Light

Double Slit Interference Applets • http: //www. walterfendt. de/ph 14 e/doubleslit. htm • http: //vsg. quasihome. com/interfer. htm

Young’s Double Slit Applet http: //www. colorado. edu/UCB/Academic. Affairs/Arts. Sciences/physics/Physics. Initiative/ Physics 2000/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 2 slits-separated by d d Single source of monochromatic light L Screen a distance L from slits

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 2 slits-separated by d d Single source of monochromatic light The rays start in phase, and travel the same distance, so they will arrive in phase. L Screen a distance L from slits

Preflight 26. 1 The experiment is modified so that one of the waves has its phase shifted by ½ l. Now, the interference will be: ½ l shift 1) Constructive 2) Destructive 3) Depends on L d Single source of monochromatic light L 2 slits-separated by d Screen a distance L from slits

Preflight 26. 1 The experiment is modified so that one of the waves has its phase shifted by ½ l. Now, the interference will be: ½ l shift 1) Constructive 2) Destructive 3) Depends on L d Single source of monochromatic light L The rays start out of phase, and travel the same distance, so they will arrive out of phase. 2 slits-separated by d Screen a distance L from slits

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

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

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

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

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

Preflight 26. 3 L y d When this Young’s double slit experiment is placed under water. The separation y between minima and maxima 1) increases 2) same 3) decreases

Preflight 26. 3 L y d When this Young’s double slit experiment is placed under water. The separation y between minima and maxima 1) increases 2) same …wavelength is shorter under water. 3) decreases

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) Yes 2) 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) Yes Need: d sin q = m l If l>d 2) No => sin q = m l / d then l /d>1 so sin q > 1 Not possible!

Reflections at Boundaries Slow Medium to Fast Medium Free End Reflection No phase change 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 1 t 2 n 0=1. 0 (air) n 1 (thin film) n 2 Get two waves by reflection off of two different interfaces. Ray 2 travels approximately 2 t further than ray 1.

Reflection + Phase Shifts Incident wave Reflected wave n 1 n 2 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

Reflection + Phase Shifts Incident wave Reflected wave n 1 n 2 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. )

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

Thin Film Practice 1 t 2 n = 1. 0 (air) nglass = 1. 5 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? d 1 = d 2 = Phase shift = d 2 – d 1 =

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? d 1 = ½ Reflection at air-film interface only d 2 = 0 + 2 t / lglass = 2 t nglass/ l 0= 1 Phase shift = d 2 – d 1 = ½ wavelength

Blue light l = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: 1 2 t n=1 (air) nglass =1. 5 nplastic=1. 8 1. Constructive 2. Destructive 3. Neither

Blue light l = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is: 1. Constructive 1 t 2 n=1 (air) nglass =1. 5 nplastic=1. 8 d 1 = ½ d 2 = ½ + 2 t / lglass = ½ + 2 t nglass/ l 0= ½ + 1 Phase shift = d 2 – d 1 = 1 wavelength 2. Destructive 3. Neither

Preflights 26. 4, 26. 5 A thin film of gasoline (ngas=1. 20) and a thin film of oil (noil=1. 45) are floating on water (nwater=1. 33). t= When the thickness of the two films is exactly one wavelength… nair=1. 0 ngas=1. 20 noil=1. 45 nwater=1. 3 The gas looks: • bright 67 % • dark 33 % The oil looks: • bright 35 % • dark 65 %

Preflights 26. 4, 26. 5 A thin film of gasoline (ngas=1. 20) and a thin film of oil (noil=1. 45) are floating on water (nwater=1. 33). t= When the thickness of the two films is exactly one wavelength… nair=1. 0 ngas=1. 20 noil=1. 45 nwater=1. 3 The gas looks: • bright • dark d 1, gas = ½ d 2, gas = ½ + 2 | d 2, gas – d 1, gas | = 2 constructive The oil looks: • bright • dark d 1, oil = ½ d 2, oil = 2 | d 2, oil – d 1, oil | = 3/2 destructive