A soap flim of thickness `0.3 mu m` appears dark when seen by the refracted light of wavelength `580 nm`. What is the index of refraction of the soap sloution, if it is known to be between `1.3` and `1.5`?

Answer

1.45

Explanation

The path difference is `2mu t`.
Now for destructive interface it can be
`2mut=(lambda)/(2)` or `(3lambda)/(2)` or `(5lambda)/(2)` and so on………
`mu=(lambda)/(4 t),(3lambda)/(4 t),(5lambda)/(4 t)……..`
`=(580xx10^(-9))/(4xx0.3xx10^(-6)) , (3xx580xx10^(-9))/(4xx0.3xx10^(-6)) .......`
`0.4833, 3xx0.4833......`
so only `mu=3xx0.4833=1.45` is the answer, `{1.3 lt mu lt 1.5}`