A thin sheen of oil (noil = 1.2) is spread over water (nwater = 1.33). White lig

Question

A thin sheen of oil (noil = 1.2) is spread over water (nwater = 1.33). White light (full spectrum/mixed wavelengths) is incident from above. You happen to be viewing from above, your eyes in air! (nair = 1, ). Determine the minimum thickness of the sheen at the places it appears intensely bright blue (take the wavelength of blue light to be 450nm in air). Suppose 450nm is the wavelength as observed within the oil layer. Repeat/revise part a. as necessary. Suppose that instead of a sheen of oil over water, we had oil over glass (nglass = 1.5). Repeat/revise part a. as necessary. Suppose that instead of a sheen of oil over water, we had a membrane of oil with air on both sides (like a soap film in a hoop). Repeat/revise part a. as necessary.

Explanation / Answer

a) The minimum thickness of the film is :

t = / 4n

t = 450 nm/ 4*1.2

t = 93.75 nm

b) The minimum thickness of the film is :

t = / 2n

t = 450 nm/ 2*1.2

t = 187.5 nm

c) The minimum thickness of the film is :

t = / 4n

t = 450 nm/ 4*1.2

t = 93.75 nm

d) The minimum thickness of the film is :

t = / 2n

t = 450 nm/ 2*1.2

t = 187.5 nm

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