1. PHY 1371Dr. Jie Zou1 Chapter 37 Interference of Light Waves (Cont.)

2. PHY 1371Dr. Jie Zou2 Outline Change of phase due to reflection Lloyd’s mirror Phase change due to reflection Interference in thin films Interference in a wedge-shaped film Newton’s rings

3. PHY 1371Dr. Jie Zou3 Lloyd’s Mirror Lloyd’s mirror: Another simple, yet ingenious, arrangement for producing an interference pattern with a single light source. Observation: An interference pattern is observed on the viewing screen. However, the positions of the dark and bright fringes are reversed relative to the pattern created by Young’s experiment. Lloyd’s Mirror

4. PHY 1371Dr. Jie Zou4 Change of phase due to reflection Explanation for the previous observation: The coherent light sources at points S and S’ differ in phase by 180° (or  rad), a phase change produced by reflection. In general, an electromagnetic wave undergoes a phase change of 180° upon reflection from a medium that has a higher index of refraction than the one in which the wave is traveling.

5. PHY 1371Dr. Jie Zou5 An analogy The general rules: An electromagnetic wave undergoes a 180° phase change when reflected from a boundary leading to an optically denser (larger n) medium. No phase change occurs when the electromagnetic wave is reflected from a boundary leading to a less optically dense (smaller n) medium.

6. PHY 1371Dr. Jie Zou6 Observation of interference effects in thin films Examples of thin films in everyday life: thin layers of oil on water or the thin surface of a soap bubble. Observation: varied colors are observed when white light is incident on such thin films. Explanation for the observation: The varied colors result from the interference of waves reflected from the two surfaces of the film.

7. PHY 1371Dr. Jie Zou7 Two factors should be considered: 1. The difference in path length for the two rays. 2. The 180° phase change upon reflection. Assumption: Normal incidence. Condition for constructive interference: 2nt = (m+1/2), m =0, 1, 2… Condition for destructive interference: 2nt = m, m = 0, 1, 2… Note: These conditions are true only when n 1 n 2 or n 1 >n<n 2,, when a net phase change of 180° due to reflection occurs. Interference in thin films

8. PHY 1371Dr. Jie Zou8 Example 37.5: Interference in a wedge-shaped film A thin, wedge-shaped film of refractive index n is illuminated with monochromatic light of wavelength. Describe the interference pattern observed for this case.

9. PHY 1371Dr. Jie Zou9 Example 37.4 Nonreflective coatings for solar cells Suppose that a silicon (si) solar cell (n = 3.5) is coated with a thin film of silicon monoxide (SiO, n= 1.45) in order to minimize reflective losses from the surface. Find the minimum film thickness that produces the least reflection at a wavelength of 550 nm, near the center of the visible spectrum.

10. PHY 1371Dr. Jie Zou10 Newton’s rings Set up: A plano-convex lens on top of a flat glass surface. The air film between the glass surfaces varies in thickness. Observation: A pattern of light and dark rings when observed from above using light of a single wavelength. Derivation for the radii of the dark rings (Problem #67): r m  (m R/n film ) 1/2, m =0, 1, 2…

11. PHY 1371Dr. Jie Zou11 Homework Ch. 37, P. 1200, Problems: #32, 33, 39, 62.