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Chapter 37

Interference of Light Waves (Cont.)

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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

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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

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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.

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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.

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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.

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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 n1<n>n2 or n1>n<n2,, when a net phase change of 180° due to reflection occurs.

Interference in thin films

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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.

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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.

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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 (mR/nfilm)1/2, m =0, 1, 2…

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Homework

Ch. 37, P. 1200, Problems: #32, 33, 39, 62.