In an interference arrangement similar to Young's double-slit experiment, the slits $S_1$ and $S_2$ are illuminated with coherent microwave sources, each of frequency ${\mathrm{10}}^6 \mathrm{Hz}.$ The sources are synchronized to have zero phase difference. The slits are separated by a distance $d=150.0 \mathrm{m}.$ The intensity $I\left(\mathrm{\theta }\right)$ is measured as a function of $\mathrm{\theta },$ where $\mathrm{\theta }$ is defined as shown. If $I_0$ is the maximum intensity, then $I\left(\theta \right)$ for $0\le \mathrm{\theta }\le 90°$ is given by :

Figure shows plane waves refracted from air to water using Huygen's principle $a, b, c, d, e$ are lengths on the diagram. The refractive index of water $\text{w.r.t.}$ air is the ratio.

A monochromatic light source of wavelength $\mathrm{\lambda }$ is placed at $S\mathit{.}$ Three slits $S_1,{ S}_2$ and $S_3$ are equidistant from the source $S$ and the point $P$ on the screen. $S_{1}P-S_{2}P=\mathrm{\lambda }/6$ and $S_{1}P-S_{3}P=\frac{2\mathrm{\lambda }}{3}.$ If $I$ be the intensity at $P$ when only one slit is open, the intensity at $P$ when all the three slits are open is-

In a Young's double slit experiment, green light is incident on the two slits. The interference pattern is observed on a screen. Which of the following changes would cause the observed fringes to be more closely spaced?

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

In a Young's Double slit experiment, first maxima is observed at a fixed point $P$ on the screen. Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point $P$ to the intensity at point $O$ (centre of the screen)-

To make the central fringe at the centre $O,$ a mica sheet of refractive index $1.5$ is introduced. Choose the correct statements $\left(s\right)-$