Physics 102: Lecture 20 Interference

1. Physics 102: Lecture 20 Interference

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

3. q q q q Angular SizePreflight 19.6, 19.7 Both are same size, but nearer one looks bigger. • 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? HighwireCaramel ApplesRabbits KindergartenHello ArboretumHalloweenAmazing

5. magnifying glass virtual image object hi ho do di 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 theangularmagnification M:

6. 1 1 1 1 1 1 + = Þ = - For the lens : d d f d f d o i o i Angular Magnification magnifying glass virtual image (dnear = near point distance from eye.) object ho hi do di For max. magnification, put image at dnear: so set di = -dnear: M = dnear /d0 = dnear/f +1 Smaller f means larger magnification

7. +1 t -1 +1 t -1 +2 t -2 Superposition ConstructiveInterference + In Phase

9. +2 t -2 Superposition Destructive Interference +1 t -1 + +1 Out of Phase 180 degrees t -1

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

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

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

14. Two different paths Single source Interference possible here 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*

15. 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

17. ½ l shift 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 d The rays start out of phase, and travel the same distance, so they will arrive out of phase. Single source of monochromatic light  L 2 slits-separated by d Screen a distance L from slits

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

19. 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.

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

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

23. 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

25. 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

26. 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.

27. 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.)

29. 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

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

31. 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? Reflection at air-film interface only d1 = d2 = Phase shift = d2 – d1 =

33. 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 d1 = d2 = Phase shift =

34. nair=1.0 t =l noil=1.45 ngas=1.20 nwater=1.3 Preflights 20.4, 20.5 A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength… • The gas looks: • bright • dark • The oil looks: • bright • dark