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. What should be the minimum thickness t which will make the intensity at the center of the fringe pattern zero?

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

Answer 1

Answer: (A)

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

Change in the optical path $=\mu t–t=(\mu –1)tb)$

To have a dark fringe at the centre the pattern should shift by one half of a fringe.

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