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Visible light of variable wavelength is ...

Visible light of variable wavelength is incident normally on a thin sheet of plastic in air. The reflected light has a minima only for `lamba=512` nm and `lambda=640` nm in the visible spectrem. What is the minimum thickness (in mum) of the film `(mu=1.28)` ?

Text Solution

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Reflected ray from upper surface would sgift by `lamda//2` only while reflected from lower surface would not have any shift.
`2mut=n_(1)lamda_(1)=n_(2)lamda_(2)rArr(n_(1)=n_(2)+1)`
as there is no minimum in between these two wavelengths
`(n+1)(512)=(n)(640)`
`n_(2)(640-512)=512`
`n_(2)=4`
`"So "2xx1.28t=(4)(640)`
`t=(4xx640)/(2xx1.28)=1000nm=1mum" "]`
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