In an ideal Young's double-slit experiment,a glass plate of thickness $t$ and refractive index $\mu = 1.5$ is placed in the path of one of the interfering beams. If the central bright fringe shifts to the position originally occupied by the first bright fringe (corresponding to wavelength $\lambda$),then the minimum thickness $t$ of the glass plate is:

In Young's double-slit experiment,if one slit is made twice as wide as the other instead of having equal widths,then in the interference pattern:

In a $YDSE$,light of wavelength $\lambda = 5000 \; \mathring{A}$ is used,which emerges in phase from two slits separated by a distance $d = 3 \times 10^{-7} \; m$. $A$ transparent sheet of thickness $t = 1.5 \times 10^{-7} \; m$ and refractive index $\mu = 1.17$ is placed over one of the slits. What is the new angular position of the central maxima of the interference pattern,and what is its linear position $y$ from the center of the screen?

In a double slit experiment,instead of taking slits of equal widths,one slit is made twice as wide as the other. Then in the interference pattern:

In the given figure,light is incident at an angle $\theta$ with the normal to a plane containing two slits of separation $d$. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle $\theta$ and outgoing angle $\phi$.

Two coherent point sources $S_1$ and $S_2$ vibrating in phase emit light of wavelength $\lambda$. The separation between them is $2 \lambda$ as shown in the figure. The first bright fringe is formed at $P$ due to interference on a screen placed at a distance $D$ from $S_1$ $(D >> \lambda)$. Find the distance $OP$.