A grease with an index of refraction of n=1.44 traps a thin layer of oil with an

Question

A grease with an index of refraction of n=1.44 traps a thin layer of oil with an index of refraction of n=1.22 on top of a glass plate with index of refraction of n=1.56.

a) If the predominant color of light reflected from white light by the oil layer has a wavelength of 692 nm in air, what can be the thinnest oil layer? Assume that the reflection is at normal incidence. Show all phase shifts and advances to justify your answer. Note: Interference from the grease layer can be neglected as it is thick.

b) Are there any wavelengths of visible light in air (380-750 nm) will not be reflected strongly by the oil layer? Show all phase shifts and advances to justify your answer.

(Points will be given to the answer that is complete and shows all the steps required)

Explanation / Answer

a)

t = thikness of the oil layer

2 t = (lambda/n)/2

t = lambda/4n = 692e-9/(4*1.22) = 1.42e-7 m

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b)

2 t = m (lambda/n) , m=1,2,3,4,5,...

lambda = 2 n t/m = 2*1.22*(1.41803e-7)/m = (346e-9)/m

No there is not.

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