A film of oil of index of refraction n = 1.43 floats on water ( n = 1.33). When

Question

A film of oil of index of refraction n = 1.43 floats on water (n = 1.33). When illuminated with white light at normal incidence, light of wavelengths 686 and 490 nm is predominant in the reflected light. Determine the minimum possible thickness of the oil film.
..... nm

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A thin layer of a transparent material with an index of refraction of 1.23 is used as a nonreflective coating on the surface of glass with an index of refraction of 1.56. What should the thickness of the material be for it to be nonreflecting for light of wavelength 480 nm?
....... nm

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A mica sheet that is 1.16 ?m thick is suspended in air. In reflected light, there are gaps in the visible spectrum at 361, 406, 464, and 541 nm. Find the index of refraction of the mica sheet.

Explanation / Answer

Given that

n =1.43

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The condition for the brightness (? =658 nm )is

            2nt = (m+ 1/2)?

               t = (2+ 1/2)(658 nm)/(2*(1.43))

                 = 575 nm

The condition for the brightness (? =470 nm )is

            2nt = (m+ 1/2)?

               t = (3+ 1/2)(470 nm)/(2*(1.43))

                 = 575 nm

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