The polarising angle of transparent medium is ' $\theta$ '. Let the speed of light in the medium be ' v '. Then the relation between ' $\theta$ ' and ' $\mathbf{v}$ ' is [ $\mathrm{c}=$ velocity of light in air]

The ratio of the distance of $n^{\text {th }}$ bright band and $\mathrm{m}^{\text {th }}$ dark band from the central bright band in an interference pattern is

A single slit diffraction pattern is formed with white light. For what wavelength of light the $4^{\text {th }}$ secondary maximum in diffraction pattern coincides with the $3^{\text {rd }}$ secondary maximum in the pattern of light of wavelength ' $\lambda$ '?

In Young's double slit experiment, the distance between the slits is 2 mm and the slits are 1 m away, from the screen. Two interference patterns can be obtained on the screen due to light of wavelength ' $\lambda_1$ ' and ' $\lambda_2$ ' respectively. The separation on the screen between the $3^{\text {rd }}$ order bright fringes on the two interference patterns is ( $\lambda_2=1.5 \lambda_1$ )