In the figure shown,if a parallel beam of light is incident on the plane of the slits at an angle such that the path difference at point $O$ is $\Delta x = d \sin \theta = d \cdot (\frac{2d/3}{d}) = \frac{2d}{3}$,and if point $O$ is a maxima for monochromatic light,then which of the following cannot be the wavelength of the incident light? [Assume $d << D, \lambda << d$]

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

To make the central fringe appear at the centre $O$ of the screen,a mica sheet of refractive index $\mu = 1.5$ is introduced in front of one of the slits. Choose the correct statement.

The minimum thickness of a mica sheet having refractive index $\mu = 3/2$,which should be placed in front of one of the slits in $YDSE$ to reduce the intensity at the center of the screen to half of the maximum intensity,is:

In the $YDSE$ shown,the two slits are covered with thin sheets having thickness $t$ and $2t$,and refractive index $2\mu$ and $\mu$ respectively. Find the position $(y)$ of the central maxima.

While conducting the Young's double slit experiment,a student replaced the two slits with a large opaque plate in the $x-y$ plane containing two small holes that act as two coherent point sources $(S_1, S_2)$ emitting light of wavelength $600 \ nm$. The student mistakenly placed the screen parallel to the $x-z$ plane (for $z>0$) at a distance $D=3 \ m$ from the mid-point of $S_1 S_2$,as shown schematically in the figure. The distance between the sources $d=0.6003 \ mm$. The origin $O$ is at the intersection of the screen and the line joining $S_1 S_2$. Which of the following is(are) true of the intensity pattern on the screen?
$(A)$ Straight bright and dark bands parallel to the $x$-axis
$(B)$ The region very close to the point $O$ will be dark
$(C)$ Hyperbolic bright and dark bands with foci symmetrically placed about $O$ in the $x$-direction
$(D)$ Semi circular bright and dark bands centered at point $O$