Two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (A), (B), (C), and (D) as given below.

Assertion (A): Interference pattern has all maxima that are equally bright and bands are large in number in comparison to the diffraction pattern that has maxima of decreasing intensity and fewer in number.

Reason (R): Interference is the result of the superposition of the waves from two different wavefronts whereas diffraction is the result of the superposition of the wavelets from different points of the same wavefront.

Two point sources $S_1$ and $S_2$ separated by a distance $10 \mu \mathrm{m}$ emit light waves of wavelength $4 \mu \mathrm{m}$ in phase. A circular wire of radius $40 \mu \mathrm{m}$ is placed around the sources as shown in figure, then ($O$ is the centre of the circle and $O{S}_1=O{S}_2$)

Two coherent sources of sound, $S_1$ and $S_2,$ produce sound waves of the same wavelength $\lambda =1 \mathrm{m}$ are in phase. $S_1$ and $S_2$ are placed $1.5 \mathrm{m}$ apart (see fig). A listener, located at $\mathrm{L}$, directly in front of $S_2$, finds that the intensity is at a minimum when he is $2 \mathrm{m}$ away from $S_2$. The listener moves away from $S_1$, keeping the distance from $S_2$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ from $S_1$. Then $d$ is :

In a Young's double slit experiment with light of wavelength $\mathrm{\lambda ,}$ the separation of slits is $d$ and distance of screen is $D$ such that $D\gg d\gg \lambda$ . If the Fringe width is $\beta$ , the distance from point of maximum intensity to the point where intensity falls to half of the maximum intensity on either side is:

In Newton's rings experiment, obtain an expression for the radius of the ${\mathrm{n}}^{\mathrm{th}}$ dark ring.