A soap bubble with walls 414 nm thick floats in air. If this bubble is illuminat

Question

A soap bubble with walls 414 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. nm

Explanation / Answer

light hits the bubble from a lower index of refraction and emerges from the bubble to a lower index of refraction, so there is a phase difference of /2 so our minima equation becomes:

2nt = (m + 1/2) + /2
where m=0,1,2,3,... Or simply:
2t = m /n
Where m= 1,2,3,4... and t is the thickness.

m=1:
= 2*1.33*(414)/1 = 1101nm
m=2:
= 2*1.33*(414)/2 = 550.62 nm

m=3:
= 2*1.33*(414)/3 = 367 nm

only 500 nm from the spectrum will be absent (Greenish Blue Light)

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