Question

A plate thickness $t$ made of a material of refractive index $\mu$ is placed in front of one of the slits in a double-slits experiment. What should be the minimum thickness $t$ which will make the intensity at the centre of the fringe pattern zero?

• A. $\frac{\lambda }{(\mu -1)}$
• B. $(\mu -1)\frac{\lambda }{2}$
• C. $\frac{\lambda }{2(\mu -1)}$
• D. $(\mu -1)\lambda$

Answer 1

The correct option is C $\frac{\lambda }{2(\mu -1)}$

Path difference generated due to introduction of the plate,
$\Delta x=(\mu -1)t$

For the intensity at the centre to be zero, path difference generated should be, $\Delta x=\frac{\lambda }{2}$

$\Rightarrow (\mu -1)t=\frac{\lambda }{2}$

$\Rightarrow t=\frac{\lambda }{2(\mu -1)}$

Hence, option $\left(C\right)$ is correct.