1. Fundamental Physics II PETROVIETNAM UNIVERSITY FACULTY OF FUNDAMENTAL SCIENCES Vungtau, 2013 Phamj Hong Quang E-mail: quangph@pvu.edu.vn

2. Chapter 6 Pham Hong Quang Fundamental of Drilling and Production 2 Interference

3. Chapter 6 Interference Pham Hong Quang Fundamental of Drilling and Production 3 1.Superposition and Interference 2. Young’s Two-Slit Experiment 3. Interference in Reflected Waves 4.Michelson Interferometer

4. 6.1 Superposition and Interference Pham Hong Quang Fundamental of Drilling and Production 4 If two waves occupy the same space, their amplitudes add at each point. They may interfere either constructively or destructively.

5. 6.1 Superposition and Interference Pham Hong Quang Fundamental of Drilling and Production 5 Interference is only noticeable if the light sources are monochromatic (so all the light has the same wavelength) and coherent (different sources maintain the same phase relationship over space and time). If this is true, interference will be constructive where the two waves are in phase, and destructive where they are out of phase.

6. 6.1 Superposition and Interference Pham Hong Quang Fundamental of Drilling and Production 6 In this illustration, interference will be constructive where the path lengths differ by an integral number of wavelengths, and destructive where they differ by a half-odd integral number of wavelengths

7. 6.2 6.2 Young’s Two-Slit Experiment Pham Hong Quang Fundamental of Drilling and Production 7 If light consists of particles, the final screen should show two thin stripes, one corresponding to each slit. However, if light is a wave, each slit serves as a new source of “wavelets,” as shown, and the final screen will show the effects of interference. This is called Huygens’s principle.

8. 6.2 6.2 Young’s Two-Slit Experiment Pham Hong Quang Fundamental of Drilling and Production 8 As the pattern on the screen shows, the light on the screen has alternating light and dark fringes, corresponding to constructive and destructive interference. The path difference is given by:

9. 6.2 6.2 Young’s Two-Slit Experiment Pham Hong Quang Fundamental of Drilling and Production 9 The dark fringes are between the bright fringes; the condition for dark fringes is: Therefore, the condition for bright fringes (constructive interference) is:

10. 6.2 6.2 Young’s Two-Slit Experiment Pham Hong Quang Fundamental of Drilling and Production 10 This diagram illustrates the numbering of the fringes.

11. 6.2 6.2 Young’s Two-Slit Experiment Pham Hong Quang Fundamental of Drilling and Production 11 How do we locate the vertical position of the fringes on the screen? 1) L >> d 2) d >> λ These tell us that θ is small Therefore,

12. 6.2 6.2 Young’s Two-Slit Experiment Pham Hong Quang Fundamental of Drilling and Production 12

13. 6.2 6.2 Young’s Two-Slit Experiment Pham Hong Quang Fundamental of Drilling and Production 13 The intensity of light along the screen

14. 6.3 Interference in Reflected Waves Pham Hong Quang Fundamental of Drilling and Production 14 Reflected waves can interfere due to path length differences, but they can also interfere due to phase changes upon reflection.

15. 6.3 Interference in Reflected Waves Pham Hong Quang Fundamental of Drilling and Production 15 There is no phase change when light reflects from a region with a lower index of refraction. There is a half-wavelength phase change when light reflects from a region with a higher index of refraction, or from a solid surface. There is also no phase change in the refracted wave.

16. 6.3 Interference in Reflected Waves Pham Hong Quang Fundamental of Drilling and Production 16 Assume: n 1 <n 2 Condition for constructive interference Because and θ~ 0 Then Condition for destructive interference

17. 6.3 Interference in Reflected Waves Pham Hong Quang Fundamental of Drilling and Production 17 If take in account θ 1, condition for constructive interference Because We get

18. 6.3 Interference in Reflected Waves Pham Hong Quang Fundamental of Drilling and Production 18

19. 6.3 Interference in Reflected Waves Pham Hong Quang Fundamental of Drilling and Production 19 CDs (compact disks) depend on interference for their functioning. The signal is encoded as tiny bumps in the surface, and the reflected laser beam varies in intensity depending on whether it is reflecting from a bump or not.

20. 6.4 Michelson Interferometer Pham Hong Quang Fundamental of Drilling and Production 20 An interferometer works on the principle of superposition. Michelson designed an interferometer to determine the wavelength of light. Here are the basic building blocks: A monochromatic source (emitting light waves) a detector two mirrors one semitransparent mirror (often called beam splitter)

21. 6.4 Michelson Interferometer Pham Hong Quang Fundamental of Drilling and Production 21

22. 6.4 Michelson Interferometer Pham Hong Quang Fundamental of Drilling and Production 22 In order to measure the thickness l of a transparent plate with the index of refraction n Insert the plate in the path of light. The number of wavelength in two paths (forwards and backwards) within the plate is: The number of wavelength in two paths (forwards and backwards) within the same thickness but in air:

23. 23 Pham hong Quang 23 PetroVietnam Universityg Thank you!