The separation between the consecutive dark fringes in a Young's double slit experiment is $1.0 \mathrm{mm}$. The screen is placed at a distance of $2.5 \mathrm{m}$ from the slits and the separation between the slits is $1.0 \mathrm{mm}.$ Calculate the wavelength of light used for the experiment.

In a double slit interference experiment, the separation between the slits is $1.0 \mathrm{mm}$, the wavelength of light used is $5.0\times {10}^{-7} \mathrm{m}$ and the distance of the screen from the slits is $1.0 \mathrm{m}$.

$\left(a\right)$ Find the distance of the center of the first minimum from the center of the central maximum.

$\left(b\right)$ How many bright fringes are formed in one centimeter width on the screen?

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.

$\left(a\right)$ Find the change in the optical path due to introduction of the plate.

$\left(b\right)$ What should be the minimum thickness $t$ which will make the intensity at the center of the fringe pattern zero? Wavelength of the light used is $d$. Neglect any absorption of light in the plate.