A scientist notices that an oil slick floating on water when viewed from above h

Question

A scientist notices that an oil slick floating on water when viewed from above has many different colors reflecting off the surface, making it look rainbow-like. She aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). The index of refraction of water is 1.33.
a. The index of refraction of the oil is 1.2. What is the minimum thickness t of the oil slick at that spot?
b. Suppose the oil had an index of refraction of 1.5. What would the minimum thickness t be now?

Explanation / Answer

Given,

lambda(air) = 750 nm ; n(water) = 1.33

a)n(oil) = 1.2

the wavelength of light in oil will be:

lambda(oil) = lambda(air)/n(oil) = 750/1.2 = 625 nm

we know that, 2 t = m lambda

t = m lambda/2 = 1 x lambda(oil)/2

t = 625/2 = 312.5 nm

Hence, thickness = t = 312.5 nm = 313 nm

b)now the wavelength in oil with n = 1.5 will be:

lambda(oil) = 750/1.5 = 500 nm

In this case, there will be shift of a half wavelength so

2t = lambda/2

t = lambda/4 = lambda(oil)/4 = 500/4 = 125 nm

Hence, thickness = t = 125 nm

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