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

$A$ laser beam is used for carrying out surgery because it

Assertion : Different colours travel with different speed in vacuum.
Reason : Wavelength of light depends on refractive index of medium.

The figure shows $P$ and $Q$ as two equally intense coherent sources emitting radiations of wavelength $20 \, m$. The separation $PQ$ is $5.0 \, m$ and the phase of $P$ is ahead of the phase of $Q$ by $90^{\circ}$. $A, B,$ and $C$ are three distant points of observation equidistant from the mid-point of $PQ$. The intensity of radiations at $A, B,$ and $C$ will bear the ratio:

Statement $(S)$: Using Huygen's eye-piece, measurements can be taken, but they are not correct.
Reason $(R)$: The cross wires, scale, and final image are not magnified proportionately because the image of the object is magnified by two lenses, whereas the cross-wire scale is magnified by one lens only.
Identify the correct one of the following:

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 $\lambda_0 = 6000 \text{ Å}$.