When one of the slits in Young's experiment is covered with a transparent sheet of thickness $3.6 \times 10^{-3} \ cm$,the central fringe shifts to a position originally occupied by the $30^{th}$ bright fringe. If $\lambda = 6000 \ \mathring{A}$,then what is the refractive index of the sheet?

In a double-slit experiment,the wavelength $\lambda$ of the light source is $400 \ nm$,the slit separation $d$ is $20 \ \mu m$,and the individual slit width $a$ is $4 \ \mu m$. Considering the interference of light from the two slits and the diffraction of light through each slit,find the number of bright interference fringes that lie within the central peak of the diffraction envelope.

In Young's double slit experiment,if the width (aperture) of the source slit $S$ is increased while keeping other parameters constant,then the interference fringes will:

To make the central fringe at the centre $O$,a mica sheet of refractive index $1.5$ is introduced. Choose the correct statement$(s)$.

Two coherent narrow slits emitting light of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $3 \lambda$. The light is collected on a screen $S$ which is placed at a distance $D (>> \lambda)$ from the slits. Find the smallest distance $x$ from the center $O$ such that the point $P$ is a maxima.

The fringe widths are found to be $\omega_1$ and $\omega_2$ respectively if a Young's double slit experiment is performed in media of refractive indices $n_1$ and $n_2$ respectively. The correct statement is: