Find the thickness of a soap film that gives constructive second order interference of reflected red light $(\mathrm{\lambda }=7000 \AA ).$ The index of refraction of the film is 1.33. Assume a parallel beam of incident light directed at ${30}^0$ to the normal.

In a Young's double slit experiment with light of wavelength $\mathrm{\lambda ,}$ the separation of slits is $d$ and distance of screen is $D$ such that $D\gg d\gg \lambda$ . If the Fringe width is $\beta$ , the distance from point of maximum intensity to the point where intensity falls to half of the maximum intensity on either side is:

The Young's double slit experiment is performed with blue light and green light of wavelengths $4360 \mathrm{\AA }$ and $5460 \mathrm{\AA }$ respectively. If $X$ is the distance of $4^{th}$ maxima from the central one, then

A parallel beam of light is incident on a tank filled with water up to a height of $61.5 \mathrm{mm}$ as shown in the figure below. Ultrasonic waves of frequency $0.5 \mathrm{MHz}$ are sent along the length of the water column using a transducer placed at the top, and they form longitudinal standing waves in the water. Which of the schematic plots below best describes the intensity distribution of the light as seen on the screen? Take the speed of sound in water to be $1,500 \mathrm{m} {\mathrm{s}}^{-1}$.

Two coherent point sources $S_1$ and $S_2$ are separated by a small distance $d$ as shown in the figure. The fringes obtained on the screen will be