1. Physics 52 - Heat and Optics Dr. Joseph F. Becker Physics Department San Jose State University © 2005 J. F. Becker

2. Chapter 35 Interference © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

3. A snapshot of waves of frequency f and wavelength spreading out in all directions from point S 1 in all directions. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

4. (a) A snapshot of sinusoidal waves spreading out from two coherent sources S 1 and S 2. Sources in phase. (b) Constructive interference (c) Destructive interference © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

5. Constructive interference Destructive interference © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

6. Red antinodal curves (curves of maximum amplitude.) © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

7. (a) Young’s experiment showing the interference of light passing thru two slits. Geometrical analysis Geometry when R > d  © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

8. Photograph of interference fringes produced on a screen in Young’s double slit experiment. d sin  = m where m = 0, +1 +2,… © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

9. Two radio antennas broadcasting in phase. Red arrows indicate directions of maximum intensity. d sin  = m m = 0, +1 +2.  = c / f © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

10. Phasor diagram for the superposition (addition) at a point of two waves of equal amplitude E with a phase difference of . The resultant wave has amplitude of E p © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

11. Intensity distribution in the interference pattern from two identical slits. The maxima occur at points where  is an integral multiple of 2  and the path difference d = sin  is an integral multiple of. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

12. Interference between rays reflected from the upper and lower surfaces of a thin film. Constructive or destructive interference can occur depending on the film thickness. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

13. Interference between two light waves reflected from the two sides of an air wedge separating two glass plates. The path difference is 2 t. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

14. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optic THIN-FILM INTERFERENCE When light shines on a thin film of oil floating on a layer of water, two light waves (#1 and #2), enter the eye after reflection and refraction. The oil thickness t = several n ’s of light in the oil oil = vac / n  path = 2t C 2001 Wiley, Physics Cutnell & Johnson 5 th Ed.

15. NOTE: When a wave on a rope reflects from a wall, the wave undergoes a 180 o phase change. Light waves can also undergo a 180 o phase shift upon reflection depending on the reflecting surfaces. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

16. The 180 o phase change on reflection: 1.Light traveling from a larger to smaller index of refractive index has NO phase change. 2. Light traveling from smaller to a larger index of refractive index has a 180 o phase change. Larger to smaller index NO phase change Smaller to larger index 180 o phase change © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

17. THIN-FILM INTERFERENCE There is 180 o phase change at air – gas interface. There is NO phase change at the gas – water interface. oil = vac / n 180 o 0o0o  path = 2t C 2001 Wiley, Physics Cutnell & Johnson 5 th Ed. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics GAS AIR WATER

18. If there are no phase changes upon reflection constructive (max intensity) interference will occur if the top film (oil) is: 2 t = m n 2t = oil, 2 oil, 3 oil, … If there is a 180 o phase change upon reflection constructive (max intensity) interference will occur if top film (oil) is 2 t = (m + ½) n 2t + oil /2 = oil, 2 oil, 3 oil, … IMPORTANT: oil = vac / n For destructive (min intensity) interference, interchange the two equations! © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

19. If there are no phase changes upon reflection destructive (min intensity) interference will occur if top film (oil) is: 2 t = (m + ½) n 2t = ½ oil, 1.5 oil, 2.5 oil, 3.5 oil, … If there is a 180 o phase change upon reflection destructive (min intensity) interference will occur if top film (oil) is: 2 t = m n 2t + oil /2 = oil /2, 3 oil /2, 5 oil /2, … IMPORTANT: oil = vac / n © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

20. Upper figures: Light waves striking an interface between optical materials at (approximately) normal incidence. Mechanical wave pulses on ropes: NO PHASE NO REFLECTION 180 o PHASE CHANGE CHANGE n a > n b n a = n b n a < n b © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

21. A nonreflective coating has an index of refraction that is intermediate between those of glass and air. Destructive interference* occurs upon reflection when film thickness is ¼ in the film. *No reflected light here! n = 1.00 1.38 1.50 180 o © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

22. A schematic diagram of a Michelson interferometer. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

23. Review © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics