1. Thursday, Sep. 4Phy208 Lecture 2 1 From last time… Waves Interference Please pick up pack of color sheets

2. Thursday, Sep. 4Phy208 Lecture 2 2 Interference of 2 speakers crest trough constructive interference,loud tone destructive interference quit tone

3. Thursday, Sep. 3Phy208 Lecture 2 3 A little more detail Same distance, same phase Path 1 Path 2 Path-length difference  = (Path 2) - (Path 1) = 0 d Path 1 Path 2

4. Thursday, Sep. 3Phy208 Lecture 2 4 Other angles? Interference: Constructive:  =  = Extra path length d  Path 1 Path 2 Path-length difference  0 Destructive:  =

5. Thursday, Sep. 4Phy208 Lecture 2 5 Question Suppose that the frequency of the sound wave increases by a factor of two. The adjacent maxima are A) Farther apart B) Closer together C) Same D) Need to know speaker spacing Higher frequency, -> shorter wavelength Less path length diff required to make 1 wavelength diff.

6. Thursday, Sep. 3Phy208 Lecture 2 6 Question In your room you have two speakers in different corners. At your desk you are exactly 1 meter from each, so that there is no interference. Your roommate moved one of your speakers 0.25 m further away from your desk. At what frequency will you hear destructive interference? A.170 Hz B.340 Hz C.680 Hz D.1000 Hz E.1350 Hz

7. Thursday, Sep. 4Phy208 Lecture 2 7 Math Analysis Constructive interference:  = Extra path length  Path 1 Path 2 d  = 0.347 rad = 19.9˚

8. Thursday, Sep. 4Phy208 Lecture 2 8 For small angles… for constructive interference For small , with  in radians Small angle approximation e.g.Exact value: Approx breaks down for large 

9. Thursday, Sep. 4Phy208 Lecture 2 9 Light waves Light is a wave just like sound. But can propagate in vacuum –at speed c = 3x10 8 m/s Has same wave properties, e.g. Can also propagate in glass, water, but slower –Speed in medium = v = c/n –n = Index of refraction Has same superposition / interference properties

10. Thursday, Sep. 4Phy208 Lecture 2 10 Interference of light

11. Thursday, Sep. 4Phy208 Lecture 2 11 L Recording plate Projection on screen Light wavelength much shorter than sound Interference fringes much closer together Light beam Foil with two narrow slits  y

12. Thursday, Sep. 4Phy208 Lecture 2 12   = Extra path length y = position on screen = Small-angle approximation Extra path length =

13. Thursday, Sep. 4Phy208 Lecture 2 13 For bright fringes: extra path length = m For dark fringes: extra path length = (m+1/2) Fringe separation & wavelength Bright Fringe separation =

14. Thursday, Sep. 4Phy208 Lecture 2 14 Question A two-slit interference pattern is observed in air (n=1). Then the entire system is immersed in water (n=1.33). The interference fringes are A) 1.33 times closer together B) 1.33 times farther apart C) 2.66 times closer together D) 2.66 times farther apart E) Spacing unchanged

15. Thursday, Sep. 4Phy208 Lecture 2 15 Interference of multiple sources  Evenly-spaced slits have maxima at same location as two-slits.  Maxima become sharper, more intense  Interference of multiple sources often called diffraction

16. Thursday, Sep. 4Phy208 Lecture 2 16 Diffraction gratings Diffraction grating is pattern of multiple slits. Very narrow, very closely spaced. Expect very narrow interference peaks. (15,000 lines/inch)x(1 inch/2.54 cm)x(100 cm/m)=5.9x10 5 /m So a spacing of 1/(5.9x10 5 /m) = 1.7x10 -6 m = 1700 nm. 1700 nm

17. Thursday, Sep. 4Phy208 Lecture 2 17 Question Suppose white light is shined through a diffraction grating. What would the pattern on the screen look like? A) B) C) D)

18. Thursday, Sep. 4Phy208 Lecture 2 18 Diffraction: only one slit, but “wide” Huygen’s principle: each portion of the slit acts as a source of waves These sources interfere according to path-length difference.

19. Thursday, Sep. 4Phy208 Lecture 2 19 Diffraction minima Interference-like pattern from a single slit. How wide is wide?

20. Thursday, Sep. 4Phy208 Lecture 2 20 Phase difference Waves start in phase Travel different distances (extra path length =  ) No longer in phase when combined (Phase diff  )  =   =2π  = /2   =π General reln: Constructive:  =2πm Destuctive:  =2π(m+1/2)

21. Thursday, Sep. 4Phy208 Lecture 2 21 Thin film interference Black Colors changing with thickness

22. Thursday, Sep. 4Phy208 Lecture 2 22 Thin film interference If film is much thinner than wavelength, ~ no phase shift from extra path length But top reflection has 180˚ phase shift, bottom not Destructive interference for all wavelengths, film appears black air: n=1 n>1 180˚ ( π radians) phase shift no phase shift t /n

23. Thursday, Sep. 4Phy208 Lecture 2 23 Thicker parts Phase difference comes from –Phase shift from reflection (top) –Phase shift from extra path length Extra path length for normal incidence = 2t air: n=1 n>1 180˚ phase shift from reflection t vac /n Extra path length=2t Phase difference = Reflection phase shift # wavelengths in extra path length destructive air: n=1

24. Thursday, Sep. 4Phy208 Lecture 2 24 Constructive interference constructive interference destructive interference