You notice a thin layer of oil floating on the surface of a water puddle. Suppos

Question

You notice a thin layer of oil floating on the surface of a water puddle. Suppose that sunlight strikes the puddle from nearly directly overhead, and also that you are viewing the puddle from nearly directly above the puddle. You see several different regions of bright color reflected from the oil — the color varies as the oil’s thickness varies. In one particular region, the oil appears to be bright green (?air = 555 nm). If n air = 1.00, n oil = 1.65, and n water = 1.33, how thick (in nanometers) is the oil layer in that region? Since there are an infinite number of solutions, give the three thinnest answers. Show your work clearly.

Explanation / Answer

Given that

wavelength of the light is = 555 x 10^-9 m

refractive index n = 1.65

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The condition for the constructive interference is

         2nt = (m+ 1/2)

For smallest thickness m =0

       2nt = /2

So the thickness of the film is

               t = /(4n)

                 = (555nm)/(4(1.65))

                 = 84.0909090nm

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