A puddle of water is covered with an oil film that has an index of refraction wi

Question

A puddle of water is covered with an oil film that has an index of refraction with an unknown value. However, it is known that the unknown value is greater than that of water. The thickness of the oil film is such that it is the minimum thickness possible for normally incident infrared radiation with a wavelength of 846 nm to experience destructive interference in the reflected radiation. When white light is incident normal to the oil film, what wavelengths in the visible range (400 nm–700 nm) will experience constructive interference?

Explanation / Answer

let's find the thickness of the oil film

t = 0.25 (846 x 10^-9) / n ( where n is the refractive index of the oil film)

t = 0.5 ( wave length)/n

0.25 (846 x 10^-9) / n =  0.5 ( wave length)/n

wave length = 423 will experience constructive interference

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