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What is the thinnest film of oil which is  floating on a puddle of water in order...

What is the thinnest film of oil which is  floating on a puddle of water in order to have constructive interference for reflected light of wavelength 588. nm as seen from above the oil? The index of refraction, n, for air is 1.00. The index of refraction, n, for oil is 1.25. The index of refraction, n, for water is 1.33

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Answer #1

Here the ray travels from air to oil to water i.e., the ray travels from rarer to denser medium gradually and to have constructive interference of the reflected(from air, oil interface) and refracted (from oil, water interface) the optical length traversed must be equal to half of the wavelength i.e.,

n_oil is the refractive index of the oil, t is the thickness of the film and is the wavelength of the light used

Putting the values,

This is the thinnest film that can produce constructive interference.

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