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A soap film of thickness 0.0011 mm appea...

A soap film of thickness 0.0011 mm appears dark when seen by the reflected light of wavelength 580 nm.. What is the index of refraction of the soap solution, if it is known to be between 1-2 and 1.5 ?

Text Solution

Verified by Experts

The correct Answer is:
1.45
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}`
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