The Physics
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Opus in profectus

# Thin Film Interference

## Summary

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• Thin film interference occurs when light reflects multiple times off the two sides of a thin transparent material.
• Thicknesses on the order of 0.1 µm ~ 10 µm (¼λ ~ 10λ of visible light within the film) are considered "thin".
• Thin film interference can be both constructive and destructive.
• Constructive interference causes the light of a particular wavelength to increase in intensity. (It brightens a particular color like red, green, or blue.)
• Destructive interference causes the light of a particular frequency to decrease in intensity. (It darkens a particular color or brightens a secondary color like cyan, magenta, or yellow.)
• Destructive interference one side of the film is balanced by constructive interference on the other side of the film. (Thin film interference does not violate the law of conservation of energy.)
• Index of Refraction
• Light travels slower in a medium (v) than in a vacuum (c).
• The index of refraction (n) is a measure of the "slowness" of light in a medium. n = c v
• As a wave travels from one medium to another, its frequency (f) remains constant. Therefore its wavelength in a medium (λ′) is directly proportional to its speed in the medium and inversely proportional to the index of refraction of the medium. λ′ = λ n
• Thin film interference is due to phase shifts caused by…
• reflections
• A wave is reflected 180° out of phase when it tries to enter a medium with a slower speed of light (when passing from a medium with a lower index of refraction to a medium with a higher index of refraction).
• A wave is reflected in phase when it tries to enter a medium with a faster speed of light (when passing from a medium with a higher index of refraction to a medium with a lower index of refraction).
• Two 180° phase shifts cancel each other out.
• path length difference (∆ℓ)
• For waves incident normal to the film, the path length difference is twice the film thickness (∆ℓ = 2t) or whole number multiples of this value (∆ℓ = 2mt).
• For waves incident at an angle to the normal, the path length difference is longer by a factor of 1/cos θfilm, so that in general…  ∆ℓ = 2mt cos θfilm
where…  ∆ℓ = path length difference t = film thickness m = number of additional "round trips" through the film θfilm = angle of transmission within the film(measured from a line normal to the film)
• A path length difference equal to a whole number of wavelengths (0λ, 1λ, 2λ,… nλ) does not lead to a phase shift.
• A path length difference equal to an odd number of half wavelengths (½λ, 1½λ, 2½λ,… (n + ½)λ) results in a phase shift of 180°.
• The phase shifts due to both factors must be considered.
• Two 180° phase shifts cancel each other out.
• There aren't any general rules for knowing how thick a thin film should be to produce a desired effect.
antireflection
coating
soap
bubble
desired effect destructive interference on reflection for incident rays normal to the surface of the film
indexes nair < nfilm < nglass nair < nwater > nair
film thickness t = ¼λ′ t = ½λ′
mnemonic "order quarter" "bubble undouble"
Two Easy to Remember Thin Film Examples