LECTURE 17 THIN FILM INTERFERENCE

Instructor: Kazumi Tolich Lecture 17

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¨ Reading chapter 28.3 ¤ Interference in reflected waves Quiz: 1

3 Air wedge interference

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¨ Constructive interference (bright fringe)

+ = �, � = 1, 2, 3, …

¨ Destructive interference (dark fringe)

+ = � + , � = 0, 1, 2, … Newton’s rings/Demo: 1

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¨ If a lens is placed on a flat glass sheet and illuminated, interference fringes are observed due to the air film. ¨ The thickness of the air is smaller toward the center of the lens. ¨ At the center the path length difference is nearly zero, and the rays interfere mostly destructively due to one 180°-phase shift upon reflection. How does anti-reflective coating work?

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¨ Magnesium fluoride (MgF2) is often used as an antireflection coating on glass lenses.

Without anti-reflective coating With anti-reflective coating Quiz: 2 through 5

7 Example: 1

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¨ The indices of refraction of MgF2 and glass are 1.38 and 1.52. Light is incident normally

on the surface of MgF2 although the diagram shows rays at angle to show the details. What

is the thinnest film thickness of MgF2 that works on an antireflection coating for light with λ = 510 nm (near the center of the visible spectrum)? Thin-film optical coating/Demo: 2

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¨ Non-reflective coating: Coat the lens with a coating such that reflections from the first and second interfaces destructively interfere, so the reflection is suppressed. ¨ Dichroic filter: Coat the lens with a coating such that reflections from the first and second interfaces are in phase. A particular band of wavelengths is reflected and the complement is transmitted. Demo: 3

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¨ Soap Film Interference

t

π

1 n 1

Interference Example: 2

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¨ A sheet of glass having an index of refraction of 1.40 is to be coated with a film of material having a refractive index of 1.55 such that green light with a wavelength of 525 nm is preferentially transmitted. a) What is the minimum thickness of the film that will achieve this result? b) Why are other parts of the visible light spectrum not also preferentially transmitted? c) Will the transmission of any color be sharply reduced? If so, which color?