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. The point directly beneath you is colored a beautiful iridescent green. You happen to remember that the index of refraction of gasoline is 1.39 and that the wavelength of green light is about 539 nm.

Required:
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?

Answer 1

Step-by-step explanation:

This problem relates to interference in thin films.

A thin layer of gasoline ( refractive index = 1.39 ) rests on water ( 1.33 ) so for constructive interference , the condition is

2μt = (2n+1)λ/2

for n = 0

2μt = λ/2

t = λ/(4μ)

= 539 / (4 x 1.39)

= 96.94 nm .

when n = 1

t = 3λ/(4μ)

t = 3 x 96.94

= 290.82 nm

when n = 2

t = 5λ/(4μ)

t = 5 x 96.94

= 484.7 nm

b )

wave length within gasoline

= 539 / refractive index

= 539 / 1.39 nm.

= 387.77 nm