Solve Thin-Film Equations: Red Light on Oil in Water

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The discussion revolves around solving thin-film equations related to an oil film on water that reflects red light. The key formula used is 2nt = (m+1/2) λ, where n is the refractive index, t is the thickness of the oil, and λ is the wavelength of light. An initial calculation resulted in an incorrect refractive index of 0.58239, which raised concerns about its validity since it must be greater than that of water (1.33). The resolution involved recognizing that for m=0, the conditions for constructive interference must be applied alongside Snell's Law. Ultimately, the correct approach clarified the relationship between the refractive index and the speed of light in different media.
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Homework Statement



White light illuminates an oil film on water. Viewing it directly from above, it looks red. Assume that the reflected red light has a wavelength of 615 nm in air, and that the oil has a thickness of 2.640e-7 m. What is the refractive index of the oil? Assume that the refractive index of water is greater than that of the oil.

Homework Equations



2nt = (m+1/2) λ

The Attempt at a Solution



2nt = (m+1/2) λ

n = 1/2 λ/(2t) = 1/2 (615e-9)/(2*2.64e-7)

n = 0.58239

I don't know why this answer is wrong. The problem seems to be straight forward, just plug in the numbers into formula right?

If m is greater than 0 then the answer n comes out higher then the refraction index of water, 1.33, so m has to be 0 I presume?

Edit: Never mind, figured it out.
 
Last edited:
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how you figured this out? can i know?
 
A refractive index less than 1 implies that the speed of light in that medium would be faster than the speed of light in vacuum!

To solve this example, you just need to consider the constructive interference condition, and couple that with Snell's Law.
 

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