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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 1.38 and that the wavelength of green light is about 540 nm. What is the minimum possible thickness of the gasoline layer directly beneath you?

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Answer:

 

Explanation:

Point beneath you forms a beautiful iridescent green

refractive index of Gasoline [tex]n=1.38[/tex]

Wavelength of Green light is [tex]\lambda =540\ nm[/tex]

Here light first traverse from air(n=1) to gasoline , it reflects from  front surface of gasoline(n=1.38) so it suffers a phase change. After this light reflect from rear surface of gasoline and there is a decrease in refractive index(n=1.38 to n=1.33), so there is no phase change occurs .

For constructive interference

[tex]2t=(m+\frac{1}{2})\cdot \frac{\lambda }{n}[/tex]

here t= thickness of gasoline film

n=refractive index

for [tex]m=0[/tex]

[tex]t=\frac{\lambda }{4n}[/tex]

[tex]t=\frac{540}{4\times 1.38}[/tex]

[tex]t=97.82\approx 98\ nm[/tex]                                                      

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