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.

Answer 1

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 $\left(\mathrm{\mu }-1\right)t$.
$$\begin{gathered} \therefore \left(\mathrm{\mu }-1\right)t=\frac{\lambda }{2} \\ \Rightarrow t=\frac{\lambda }{2\left(\mathrm{\mu }-1\right)} \end{gathered}$$
Hence, the thickness of a plate is $\frac{\lambda }{2\left(\mathrm{\mu }-1\right)}$.