Wave Optics Questions

Young’s double slit experiment is first performed in air and then in a medium other than air. It is found that $8^{th}$ bright fringe in the medium lies where $5^{th}$ dark fringe lies in air. The refractive index of the medium is nearly:

The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda }_1=4000\text{A˚}$ and ${\lambda }_2=6000\text{A˚}$ is:

Two Polaroids $P_1$ and $P_2$ are placed with their axis perpendicular to each other. Unpolarised light $I_0$ is incident on $P_1$. A third polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its axis makes an angle $45^{\circ }$ with that of $P_1$. The intensity of transmitted light through $P_2$ is: