What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble?

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What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble?

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Problem Details:

A soap bubble is essentially a thin film of water surrounded by air. The colors you see in soap bubbles are produced by interference. 


  • (a) What visible wavelengths of light are strongly reflected from a 390 nm -thick soap bubble? 
  • (b) What color would a 390 nm thick soap bubble appear to be (green, purple, or yellow)?


Question:

A soap bubble is essentially a thin film of water surrounded by air. The colors you see in soap bubbles are produced by interference. What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble? What color would such a soap bubble appear to be?

Solution 1:




What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble?

Result:


Solution 2:

Constructive interference in thin films (when the film material has a higher index of refraction):





(a)


Refractive index of water, η = 1.33


d = 390 nm (10-9m/1nm) = 390 × 10-9 m


Solving for the wavelength, λ:


λ = 2nd/(m + 1/2)


Calculating  λ when m = 1:


λ = 2nd/(m + 1/2) = 2 × 1.33 × 390 × 10-9 /(1 + 1/2) = 692 × 10-9 m(1nm/10-9m) = 692 nm


Calculating  λ when m = 2:


λ = 2nd/(m + 1/2) = 2 × 1.33 × 390 × 10-9 /(2 + 1/2) = 415 × 10-9 m(1nm/10-9m) = 415 nm


The wavelengths of viscible light that are strongly reflected are 692 nm and 415 nm.


(b)


692 nm wavelength corresponds to color red.


415 nm Corresponds to violet.


Mixing red and violet colors yields purple.


The soap bubble will appear purple.


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