Physics 102: Lecture 20 Interference 1

Unaided Eye Bring object as close as possible (to near point dnear) How big the object looks with unaided eye. object h0 q dnear Bring object as close as possible (to near point dnear) **If q is small and expressed in radians.

Angular Size Preflight 19.6, 19.7 Both are same size, but nearer one looks bigger. q q q q Angular size tells you how large the image is on your retina, and how big it appears to be. How small of font can you read? Highwire Caramel Apples Rabbits Kindergarten Hello Arboretum Halloween Amazing

Magnifying Glass object virtual image hi ho di do magnifying glass Magnifying glass produces virtual image behind object, allowing you to bring object to a closer do: and larger q′ Compare to unaided eye: : Ratio of the two angles is the angular magnification M:

Angular Magnification magnifying glass virtual image object (dnear = near point distance from eye.) hi ho do di For the lens : 1 d o + i = f Þ - For max. magnification, put image at dnear: so set di = -dnear: M = dnear /d0 = dnear/f +1 Smaller f means larger magnification

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

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

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

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

Interference for Sound … For example, a pair of speakers, driven in phase, producing a tone of a single f and l: hmmm… I’m just far enough away that l2-l1=l/2, and I hear no sound at all! l1 l2 Demo 440 Sound Interference But this won’t work for light--can’t get coherent sources

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* Single source Two different paths Interference possible here

ACT: Young’s Double Slit Light waves from a single source travel through 2 slits before meeting on a screen. The interference will be: Constructive Destructive Depends on L d Single source of monochromatic light  L 2 slits-separated by d Screen a distance L from slits

Preflight 20.1 The experiment is modified so that one of the waves has its phase shifted by ½ l. Now, the interference will be: Constructive Destructive Depends on L ½ l shift d The rays start out of phase, and travel the same distance, so they will arrive out of phase. 60% got this correct Single source of monochromatic light  L 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, l,2l, …, the screen is bright. (constructive) 2 slits-separated by d d At points where the difference in path length is the screen is dark. (destructive) Demo 162 2 slit Single source of monochromatic light  L Screen a distance L from slits

Young’s Double Slit Key Idea 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.

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

Young’s Double Slit Quantitative A little geometry… sin(q)  tan(q) = y/L Constructive interference Destructive interference where m = 0, or 1, or 2, ... 33

Preflight 20.3 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 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

Thin Film Interference 1 2 n0=1.0 (air) n1 (thin film) t n2 Demo 70 soap film Get two waves by reflection off two different interfaces. Ray 2 travels approximately 2t further than ray 1.

Reflection + Phase Shifts Incident wave Reflected wave n1 n2 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.)

Note: this is wavelength in film! (lfilm= lo/n1) Thin Film Summary Determine d, number of extra wavelengths for each ray. 1 2 n = 1.0 (air) n1 (thin film) t n2 This is important! Note: this is wavelength in film! (lfilm= lo/n1) Reflection Distance 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

Thin Film Practice (ACT) Example 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? A) d1 = 0 B) d1 = ½ C) d1 = 1 What is d1, the total phase shift for ray 1

Thin Film Practice Example 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? d1 = Reflection at air-film interface only d2 = Phase shift = d2 – d1 =

ACT: 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 Brian Dvorkin has had good luck with the following presentation. 1) Look for the ½ wavelength shifts on reflection. Then ask for constructive interference what do I need ray 2 to do? (0 or ½ wavelength more?) If choose 0, increase to 1. d1 = d2 = Phase shift =

Preflights 20.4, 20.5 t = l nwater=1.3 ngas=1.20 nair=1.0 noil=1.45 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