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Question
Find the thickness of a plate which will produce a change in optical path equal to half the wavelength λ of the light passing through it normally. The refractive index of the plate is μ.
Solution
Given
The refractive index of the plate is \[\mu.\]
Let the thickness of the plate be 't' to produce a change in the optical path difference of \[\frac{\lambda}{2}.\]
We know that optical path difference is given by \[\left( \mu - 1 \right)t.\]
\[\therefore \left( \mu - 1 \right)t = \frac{\lambda}{2}\]
\[ \Rightarrow t = \frac{\lambda}{2\left( \mu - 1 \right)}\]
Hence, the thickness of a plate is \[\frac{\lambda}{2\left( \mu - 1 \right)}.\]
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