The thickness of a plate having refractive in | vedclass

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Question

(D) Let $t$ be the thickness of the plate.When light passes through a plate of thickness $t$ and refractive index $\mu$,the optical path length is $\m

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$\frac{\lambda}{2(\mu-1)}$

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(D) Let $t$ be the thickness of the plate.When light passes through a plate of thickness $t$ and refractive index $\mu$,the optical path length is $\mu t$.The optical path length in air for the same distance $t$ is $t$.The change in optical path (optical path difference) is given by $\Delta = \mu t - t = (\mu - 1)t$.According to the problem,this change in optical path is equal to half the wavelength,i.e.,$\Delta = \frac{\lambda}{2}$.Equating the two expressions: $(\mu - 1)t = \frac{\lambda}{2}$.Solving for $t$,we get $t = \frac{\lambda}{2(\mu - 1)}$.

The thickness of a plate having refractive index $\mu$ which will produce a change in optical path equal to half the wavelength $\lambda$ of the light passing through it is

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