A soap bubble with walls 308 nm thick floats in air. If this bubble is illuminat

Question

A soap bubble with walls 308 nm thick floats in air. If this bubble is illuminated perpendicularly with sunlight, what wavelength will be absent in the reflected light? Assume that the index of refraction of the soap film is 1.33. The visible electromagnetic spectrum, along with representative wavelengths, is shown in our diagram. In addition to the wavelengths of 700.0 nm for red light and 400.0 nm for violet light, we include 600.0 nm for yellowish orange light and 500.0 nm for greenish blue light.

Explanation / Answer

thickness (d) = 308 nm, index n = 1.33
absent means destructive interference
2nd + /2 = (2k + 1)/2
2nd = k
2*1.33*308 nm = k
k = 819.28 nm
k = 1, = 819.28 nm (invisible)
k = 2, = 409.64 nm
k = 3, = 273.1 nm (invisible)
so the required wavelength is 409.64 nm

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