Looking straight downward into a rain puddle whose surface is covered with a thi

Question

Looking straight downward into a rain puddle whose surface is covered with a thin film of gasoline, you notice a swirling pattern of colors caused by interference inside the gasoline film. At that point you happen to remember that the index refraction of gasoline is 1.38 and that the wavelength of green light is about 538nm.

a.)

What are the three smallest possible thicknesses of the gasoline layer directly beneath you?

b.)

How do these thicknesses compare to the wavelength in the film?

Note: Please give details on how to approch this problem thanks

Explanation / Answer

Note that the path difference will be

2 n d = m (wavelength)

to get constructive interference.

--> d = m (wavelength) / [2 n]

For m = 1, 2, 3,

d = 195 nm, 390 nm, 585 nm   [ANSWERS, PART A]

******************

These thicknesses are comparable to the wavelengths in the film, as they have the same order of magnitude. [ANSWER, PART B]

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