Four light waves are represented by:-
$\left(i\right)$ $y=a_1\sin \omega t$
$\left(ii\right)$ $y=a_2\sin (\omega t+\epsilon )$
$\left(iii\right)$ $y=a_1\sin 2\omega t$
$\left(iv\right)$ $y=a_2\sin 2(\omega t+\epsilon )$
Interference fringes may be observed due to superposition of

While conducting the Young's double-slit experiment, a student replaced 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 $600 \mathrm{nm}.$ The student mistakenly placed the screen parallel to the $x-z$ plane $(z> 0)$ at a distance$D= 3 \mathrm{m}$ from the mid-point of$S_1{S}_2,$as shown schematically in the figure. The distance between the sources $d=0.6003 \mathrm{mm}$. 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?

Two coherent monochromatic point sources $S_1$ and $S_2$ of wavelength $\mathrm{\lambda }= 600 \mathrm{nm}$are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance $d= 1.8 \mathrm{mm}.$ This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $∆\mathrm{\theta }.$ Which of the following options is/are correct? 

In Young's double-slit experiment, the distance between slits is $d = 0.25 \mathrm{cm}$ and the distance of the screen $D = 120 \mathrm{cm}$ from the slits. If the wavelength of light used is $\lambda =6000 \stackrel{°}{\mathrm{A}}$ and $I_0$ is the intensity of central maximum, then the minimum distance of the point from the centre, where the intensity is $\frac{I_0}{2}$ is $k\times {10}^{-5} \text{m}$. What is the value of $k$?