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

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 $\lambda_0 = 6000 \text{ Å}$.

$A$ source of light emits a continuous stream of light energy which falls on a given area. Luminous intensity is defined as

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:

$A$ carrot looks orange in colour because of the $\beta$-carotene molecule in it. This means that the $\beta$-carotene molecule absorbs light of wavelengths

Answer the following questions:
$(a)$ When a low flying aircraft passes overhead,we sometimes notice a slight shaking of the picture on our $TV$ screen. Suggest a possible explanation.
$(b)$ As you have learnt in the text,the principle of linear superposition of wave displacement is basic to understanding intensity distributions in diffraction and interference patterns. What is the justification of this principle?