Question

a plate of thickness t made of a material of refractive index $\mu$ is placed in front of one of the slits in a double slit experiment (a) Find the change in th eoptical path due to introduction of th 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

(a) Change in th eopitcal path $=\mu t-t$ = $(\mu =1)t$
(b) To have a dark fringe at the center the pattern should shift by one half of a fringe.
$(\mu -1)t=\frac{\lambda }{2}\Rightarrow t=\frac{\lambda }{2(\mu -1)}$