Fundamental Physics II

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

2. Chapter 6 Interference Pham Hong QuangFundamental of Drilling and Production

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

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

5. 6.1 Superposition and Interference 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. Pham Hong Quang Fundamental of Drilling and Production

6. 6.1 Superposition and Interference 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 Pham Hong Quang Fundamental of Drilling and Production

7. 6.2Young’s Two-Slit Experiment 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. Pham Hong Quang Fundamental of Drilling and Production

8. 6.2Young’s Two-Slit Experiment 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: Pham Hong Quang Fundamental of Drilling and Production

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

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

11. 6.2Young’s Two-Slit Experiment 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, Pham Hong Quang Fundamental of Drilling and Production

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

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

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

15. 6.3 Interference in Reflected Waves 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. Pham Hong Quang Fundamental of Drilling and Production

16. 6.3 Interference in Reflected Waves and θ~ 0 Assume: n1<n2 Condition for constructive interference Because Then Condition for destructive interference Pham Hong Quang Fundamental of Drilling and Production

17. 6.3 Interference in Reflected Waves If take in account θ1, condition for constructive interference Because We get Pham Hong Quang Fundamental of Drilling and Production

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

19. 6.3 Interference in Reflected Waves 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. Pham Hong Quang Fundamental of Drilling and Production

20. 6.4 Michelson Interferometer 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) Pham Hong Quang Fundamental of Drilling and Production

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

22. 6.4 Michelson Interferometer 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: Pham Hong Quang Fundamental of Drilling and Production

23. Thank you! • Pham hongQuang23PetroVietnamUniversityg