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 \[\left( \mu - 1 \right)t.\]

\[\therefore   \left( \mu - 1 \right)t = \frac{\lambda}{2}\]

\[ \Rightarrow t = \frac{\lambda}{2\left( \mu - 1 \right)}\]

Hence, the thickness of a plate is \[\frac{\lambda}{2\left( \mu - 1 \right)}.\]