1. Chapter 37 Interference of Light Waves (Cont.) Dr. Jie Zou

2. 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 Dr. Jie Zou

3. 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 Dr. Jie Zou

4. 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. Dr. Jie Zou

5. 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. Dr. Jie Zou

6. 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. Dr. Jie Zou

7. Interference in thin films • Two factors should be considered: • The difference in path length for the two rays. • 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 n1<n>n2 or n1>n<n2,, when a net phase change of 180° due to reflection occurs. Dr. Jie Zou

8. 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. Dr. Jie Zou

9. 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. Dr. Jie Zou

10. 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): rm  (mR/nfilm)1/2, m =0, 1, 2… Dr. Jie Zou

11. Homework • Ch. 37, P. 1200, Problems: #32, 33, 39, 62. Dr. Jie Zou