A mixture of light, consisting of wavelength $590 \mathrm{nm}$ and an unknown wavelength, illuminates Young's double-slit setup and gives rise to two overlapping interference patterns on the screen. The central maximum of both patterns coincide. Further, it is observed that the third bright fringe of known light coincides with the 4^th bright fringe of the unknown light. From this data, the wavelength of the unknown light is

Using monochromatic light of wavelength $\lambda$, an experimentalist sets up the Young's double slit experiment in three ways as shown.
If she observes that $y={\beta }^{\prime }$, the wavelength of light used is :

 

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 $1,500 \mathrm{m} {\mathrm{s}}^{-1}$.