Problem: A soap bubble is essentially a very thin film of water (n = 1.33) surrounded by air. The colors that you see in soap bubbles are produced by interference. Derive an expression for the wavelengths λC for which constructive interference causes a strong reflection from a soap bubble of thickness d. Hint: Think about the reflection phase shifts at both boundaries. 

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Phase shifts occurring on a reflecting surface:

Δ = 0 if η1 > η2 and Δ = π is η1 < η2 

For the top surface of the film, η1 < η2

ɸ1 = kx1 + ɸ10 + Δ = kx1 + ɸ10 + π

For the lower surface of the film:

ɸ2 = kx2 + ɸ20 + Δ = kx1 + ɸ10 + 0

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Problem Details

A soap bubble is essentially a very thin film of water (n = 1.33) surrounded by air. The colors that you see in soap bubbles are produced by interference. 

Derive an expression for the wavelengths λC for which constructive interference causes a strong reflection from a soap bubble of thickness d. 

Hint: Think about the reflection phase shifts at both boundaries. 

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