Thin Film Problem

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Homework Statement


A thin film of alcohol (n=1.36) lies on a flat glass plate (n=1.51). When monochromatic light whose wavelength can be changed, is incident normally, the reflected light is minimum for λ=512 nm and a maximum for λ=640 nm. What is the thickness of the film?


Homework Equations


λ_n=λ/n


The Attempt at a Solution


Let the thickness be t, then we have
t/(512/1.36)=m+1/2 where m is an integer.
t/(640/1.36)=n where n is an integer.
Solving for t and setting the expressions equal, we get 376m+188=471n (using significant figures). I feel like I'm doing something wrong because of the resulting equation. Can someone help me? Thanks.
 

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