A soap bubble is 77.1 nm thick and illuminated by white light incident perpendicular to its surface. What wavelength (in nm) and color of visible light is most constructively reflected, assuming the same index of refraction as water (nw

0.41 μm or 410 nm

Explanation:

Given that

Soap thickness, t = 77.1 nm = 77.1*10^-9 m

Refractive index of water, μ = 1.33

The longest wavelength for constructive wavelength is given by the formula

2μt = (n - 1/2)λ

Making λ the subject of the formula gives

λ = 2μt / (n - 1/2), substituting the values, we have

λ = (2 * 1.33 * 77.1*10^-9) / 1/2

λ = (2.66 * 77.1*10^-9) / 1/2

λ = 2.05*10^-7 / 1/2

λ = 4.10*10*^-7 m

λ = 0.41 μm

The longest wavelength requested therefore is 0.41 μm or 410 nm

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