Consider a system of three connected strings, $S_1, S_2$ and $S_3$ with uniform linear mass densities $\mu$ $\mathrm{kg} / \mathrm{m}, 4 \mu \mathrm{~kg} / \mathrm{m}$ and $16 \mu \mathrm{~kg} / \mathrm{m}$, respectively, as shown in the figure. $S_1$ and $S_2$ are connected at the point $P$, whereas $S_2$ and $S_3$ are connected at the point $Q$, and the other end of $S_3$ is connected to a wall. A wave generator 0 is connected to the free end of $S_1$. The wave from the generator is represented by $y=y_0 \cos (\omega t-k x) \mathrm{cm}$, where $y_0, \omega$ and $k$ are constants of appropriate dimensions. Which of the following statements is/are correct:

A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index $n_{2}$. The other slit is at the interface of this medium with another medium 1 of refractive index $n_{1}\left(\neq n_{2}\right)$. The line joining the slits is perpendicular to the interface and the distance between the slits is $d$. The slit widths are much smaller than $d$. A monochromatic parallel beam of light is incident on the slits from medium 1. A detector is placed in medium 2 at a large distance from the slits, and at an angle $\theta$ from the line joining them, so that $\theta$ equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.

Which of the following statement(s) is(are) correct?

In the Young's double-slit experiment using a monochromatic light of wavelength $\lambda$, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is

Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe widths recorded are $\beta$_G, $\beta$_R and $\beta$_B, respectively. Then,

A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence $\theta$. The reflected (R) and transmitted (T) intensities, both as function of $\theta$, are plotted. The correct sketch is

Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits S$_1$ and S$_2$. In each of these cases, S$_1$P$_0$ = S$_2$P$_0$, S$_1$P$_1$ $-$ S$_2$P$_1$ = $\lambda/4$ and S$_1$P$_2$ $-$ S$_2$P$_2$ = $\lambda/3$, where $\lambda$ is the wavelength of the light used. In the cases B, C and D, a transparent sheet of refractive index $\mu$ and thickness t is pasted on slit S$_2$. The thickness of the sheets are different in different cases. The phase difference between the light waves reaching a point P on the screen from the two slits is denoted by $\delta$(P) and the intensity by I(P). Match each situation given in Column I with the statement(s) in Column II valid for that situation:

	Column I		Column II
(A)		(P)	$\delta ({P_0}) = 0$
(B)	$(\mu-1)t=\lambda/4$	(Q)	$\delta ({P_1}) = 0$
(C)	$(\mu-1)t=\lambda/2$	(R)	$I({P_1}) = 0$
(D)	$(\mu-1)t=3\lambda/4$	(S)	$I({P_0}) > I({P_1})$
		(T)	$I({P_2}) > I({P_1})$

In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is $\lambda$. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).

Speed of the light is