In a medium the speed of light wave decreases to 0.2 times to its speed in free space. The ratio of relative permittivity to the refractive index of…

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is $\_\_\_\_$. $\left(\tan ^{-1}(1.52)=57.7^{\circ}\right.$, refractive indices of air and glass are 1.00 and 1.52, respectively.)

A ray of light passing through an equilateral prism is having velocity $2.12 \times 10^8$ m/s in the prism material, then the minimum angle of deviation is _________ degrees.

In a Young double slit experiment, the wavelength of incident light is $6000$ Å, the separation between slits $S_1$ and $S_2$ is $5$ cm and the distance between slits plane and screen is $50$ cm, as shown in the figure below. If the resultant intensity at $P$ is equal to the intensity due to individual slits, the path difference between interfering waves is __________ Å. 

In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slits separations and that of the wavelengths of light used are $2: 1$ and $1: 2$ respectively. The corresponding ratio of the distances between the slits and the respective screens ($D_{1} / D_{2}$) is $\_\_\_\_$.

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at $30$ cm above the paper. If the radius of curvature of the lens is $60$ cm then the refractive index of the lens material is $\dfrac{\alpha}{10}$. The value of $\alpha$ is _______.