Question

A plate of thickness t made of a material of refractive index µ is placed in front of one of the slits in a double slit experiment. (a) Find the change in the optical path due to introduction of the plate. (b) What should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero? Wavelength of the light used is $\lambda$. Neglect any absorption of light in the plate.

Answer 1

Given:
Refractive index of the plate is μ.
The thickness of the plate is t.
Wavelength of the light is λ.
(a)
When the plate is placed in front of the slit, then the optical path difference is given by $\left(\mathrm{\mu }-1\right)t$.

(b) For zero intensity at the centre of the fringe pattern, there should be distractive interference at the centre.
So, the optical path difference should be = $\frac{\lambda }{2}$
$$\begin{gathered} \mathrm{i}.\mathrm{e}.\left(\mu -1\right)t=\frac{\lambda }{2} \\ \Rightarrow t=\frac{\lambda }{2\left(\mu -1\right)} \end{gathered}$$