Major Concepts in Physics Lecture 3.

1. Major Concepts in Physics Lecture 3. Prof Simon Catterall Office 309 Physics, x 5978 smc@physics.syr.edu http://physics/courses/PHY102.08Spring PHY102

2. Today … • Announcements • Interference – why light is a wave! • Phase difference, constructive and destructive interference • Examples: sound, Young’s double slit experiment, thin films PHY102

3. Clickers • We will NOT be using clickers this semester • Registration costs • Unnecessary since do not plan to use for grading • If anyone has bought one for this semester you should return it to the bookstore. • Instead use flashcards PHY102

4. Homeworks etc • Collect homework 1 in workshop this week. • Due 2 weeks from now in workshop PHY102

5. Interference • Phenomena that results from applying principle of superposition to (usually) 2 coherent sources of waves • Typically waves originate from two different locations PHY102

6. Coherence • Two waves are coherent if they maintain a fixed phase relationship to each other PHY102

7. Phase • Phase difference is the angle (in radians) between corresponding wave crests • If phase difference is • 0 or multiple of 2p – constructive interference • p or odd multiple – destructive interference • Typically independent sources are NOT coherent – eg. do NOT see interference from 2 light bulbs …. PHY102

8. The resulting amplitude and intensity are: PHY102

9. The resulting amplitude and intensity are: PHY102

10. Example: sound from speakers • Two loudspeakers powered from same source (coherent). • Swap polarity – phase difference now 180 degrees (p radians) – volume drops! PHY102

11. When both waves travel in the same medium the interference conditions are: For constructive interference where m = an integer. For destructive interference where m = an integer. PHY102

12. Example (text problem 25.1): A 60.0 kHz transmitter sends an EM wave to a receiver 21 km away. The signal also travels to the receiver by another path where it reflects from a helicopter. Assume that there is a 180 phase shift when the wave is reflected. (a) What is the wavelength of this EM wave? PHY102

13. Example continued: (b) Will this situation give constructive interference, destructive inference, or something in between? The path length difference is l = 10 km = 2, a whole number of wavelengths. Subtlety: a wave reflecting off a dense medium suffers an additional 180 degree phase shift. Since there is also a 180 phase shift there will be destructive interference. PHY102

14. P S1  d S2 Coherent waves can become out of phase if they travel different distances to the point of observation. This represents the extra path length (l) that the wave from S2 must travel to reach point P (P far away) PHY102

15. Young’s fringes • Single slit provides two independent coherent light sources • On distant screen see alternating bright and dark lines – corresponding to points where constructive and destructive interference takes place • Note how separation of slits affects fringe separation … PHY102

16. The pattern seen on the screen There are alternating bright/dark spots. An intensity trace PHY102

17. The bright spots occur where there is constructive interference: where m is an integer and is called the “order”. The dark spots occur where there is destructive interference: PHY102

18. Fig. 25.21 PHY102

19. The screen is far away compared to the distance between the slits (D>>d) so tan  sin  . Here, The distance between two adjacent minima is: PHY102

20. Thin Films • When light hits eg thin layer of oil on surface of water – get air/oil reflected wave r1 • Happens at oil/water interface too – r2 • Can get interference from different waves from different path lengths • Depending on wavelength may get constructive or destructive interference – selects out certain colors … PHY102

21. A light ray can be reflected many times within a medium. PHY102

22. Water Oil Air Example (text problem 25.18): A thin film of oil (n=1.50) of thickness 0.40 m is spread over a puddle of water (n=1.33). For which wavelength in the visible spectrum do you expect constructive interference for reflection at normal incidence? Consider the first two reflected rays. r1 is from the air-oil boundary and r2 is from the oil-water boundary. Incident wave r1 has a 180 phase shift (noil >nair), but r2 does not (noil<nwater). PHY102

23. Example continued: To get constructive interference, the reflected waves must be in phase. For this situation, this means that the wave that travels in oil must travel an extra path equal to multiples of half the wavelength of light in oil. The extra path distance traveled is 2d, where d is the thickness of the film. The condition for constructive interference here is: Only the wavelengths that satisfy this condition will have constructive interference. PHY102

24. Example continued: Make a table: All of these wavelengths will show constructive interference, but it is only this one that is in the visible portion of the spectrum – color ?? PHY102

25. Butterfly wing • Iridescent color because of same phenomena! • Path length depends on viewing angle – different colors at different angles … PHY102