In a YDSE, fringes are produced by monochromatic light of wavelength $5450 \mathrm{A}.$ A thin plate of glass of refractive index $1.5$ is placed normally in the path of one of the interfering beams and the central bright band of the fringe system is found to move into the position previously occupied by the third band from the centre. Select the correct alternative

A cylindrical wave front $ABC$ centred at $O$ (symmetric about $BE$ ) is incident on slits $S_1, S_2.$ $B{S}_1=S_{1}O=8\lambda$ where $\lambda$ is wavelength of light used. A slab of thickness $t$ and refractive index $\frac{4}{3}$ is placed in front of one of the slits to obtain central maxima at point $D$ (symmetrically located with respect to slits). If $t$ is least, then

A ray of light of intensity $I_0$ is incident on a parallel glass slab at point $P$ as shown. It undergoes partial reflection and refraction. At each reflection $40\%$ of incident energy is reflected. The rays $PQ$ and $P\text{'}Q\text{'}$ undergo interference. If for constructive interference, intensity is $I_1$ and for destructive interference, intensity is $I_2,$ then

In the arrangement shown in the figure, the point source $S$ oscillates about point $O$ along central axis in small amplitude. The fringes are formed on the screen

Two coherent point sources $A$ and $B$ are at separation $d=\frac{3\lambda }{2},$ where $\lambda$ is wavelength of light emitted by these sources. The oscillations of source $B$ lag in phase behind the oscillations of source $A$ by $\pi .$ The point $P$ is at angular position $\theta$ as indicated in figure. Then

A monochromatic light source $S$, is placed between a mirror and a screen as shown in the figure below,

In YDSE set up one of the slit $S_1$ of a double slit system is wider than the other, so that the amplitude of light reaching the central part of the screen from one slit acting alone is twice that from the other slit acting alone. If $d=4\lambda ,$ maximum value of $\sin \theta$ so that intensity at point $P$ is equal to average intensity on screen
is $\left(\frac{N}{16}\right).$ Find the value of $\mathrm{N}.$