Young's Double Hole Experiment

Q. In Young's double slit experiment, the distance of the $n^{th}$ dark fringe from the centre is-

1. $n\left(\frac{\lambda D}{2D}\right)$
2. $n\left(\frac{2d}{\lambda D}\right)$
3. $(2n-1)\left(\frac{\lambda D}{2d}\right)$
4. $(2n-1)\left(\frac{4d}{\lambda D}\right)$

Q. Two small angled transparent prisms (each of refracting angle $A=1^{\circ }$) are so placed that their bases coincide, so that common base is BC. This device is called Fresnel’s biprism and is used to obtain coherent sources of a point source S illuminated by monochromatic light of wavelength $6000\stackrel{\circ }{A}$ placed at a distance $a=20\text{cm}$. Calculate the separation between coherent sources. If a screen is placed at a distance $b=80$\text{cm}\) from the device, what is the fringe width of fringes (in cm) obtained
(Refractive index of material of each prism = 1.5).

Q. Consider a usual set-up Young's double slit experiment with slits of equal intensity as shown in the figure. Take $O$ as origin and the $y$-axis as indicated. If average intensity of light at all points between $y_1=-\frac{\lambda D}{4d}$ and $y_2=+\frac{\lambda D}{4d}$ equals $n$ times the intensity of central maxima, then $n$ equals (take average over phase difference)

1. $\frac{1}{2}(1+\frac{2}{\pi })$
2. $2(1+\frac{2}{\pi })$
3. $(1+\frac{2}{\pi })$
4. $\frac{1}{2}(1-\frac{2}{\pi })$

Q. In the arrangement shown in figure, slits $S_1$ and $S_4$ are having a variable separation Z. Point O on the screen is at the common perpendicular bisector of $S_1{S}_2$ and $S_3{S}_4$.
When $Z=\frac{\lambda D}{2d^{\prime }}$ the intensity measured at O is $I_0$. The intensity at O when $Z=\frac{2\lambda D}{d}$ is

1. $I_0$
2. $2I_0$
3. $3I_0$
4. $4I_0$