Two monochromatic (wavelength $\lambda = a/5$) and coherent sources of electromagnetic waves are placed on the $x$-axis at the points $(2a, 0)$ and $(-a, 0)$. $A$ detector moves in a circle of radius $R (R \gg 2a)$ whose center is at the origin. The number of maximas detected during one circular revolution by the detector are

$A$ screen receives $3 \ W$ of radiant flux of wavelength $6000 \ \mathring{A}.$ One lumen is equivalent to $1.5 \times 10^{-3} \ W$ of monochromatic light of wavelength $5550 \ \mathring{A}.$ If the relative luminosity for $6000 \ \mathring{A}$ is $0.685$ while that for $5550 \ \mathring{A}$ is $1.00,$ then the luminous flux of the source is:

The figure shows a schematic diagram of the arrangement of Young's Double Slit Experiment. Choose the correct statement$(s)$ related to the wavelength of light used.

Evidence for the wave nature of light cannot be obtained from

The difference in the number of wavelengths,when yellow light propagates through air and vacuum columns of the same thickness,is one. Find the thickness of the air column. Given: Refractive index of air $\mu_a = 1.0003$,Wavelength of yellow light in vacuum $\lambda_0 = 6000 \text{ Å}$.

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 thicknesses 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 $II$
$(A)$ No sheet	$(p)$ $\delta(P_0) = 0$
$(B)$ $(\mu-1)t = \lambda / 4$	$(q)$ $\delta(P_1) = 0$
$(C)$ $(\mu-1)t = \lambda / 2$	$(r)$ $I(P_1) = 0$
$(D)$ $(\mu-1)t = 3\lambda / 4$	$(s)$ $I(P_0) > I(P_1)$
	$(t)$ $I(P_2) > I(P_1)$