In case of diffraction, if $a$ is a slit width and $\lambda$ is the wavelength of the incident light, then the required condition for diffraction to take place is

If a microscope is placed in air, the minimum separation of two objects seen as distinct is $6 \mu \mathrm{~m}$. If the same is placed in a medium of refractive index 1.5, then the minimum separation of the two objects to see as distinct is

In Young's double slit experiment two slits are placed 2 mm from each other. Interference pattern is observed on a screen placed 2 m from the plane of the slits. Then the fringe width for a light of wavelength 400 nm is

In Young's double slit experiment, the intensity at a point where the path difference is $\frac{\lambda}{6}$ ( $\lambda$ being the wavelength of the light used) is $I$. If $I_0$ denotes the maximum intensity, $\frac{I}{I_0}$ is equal to