$A$ plane polarized light is incident on a polarizer with its pass axis making an angle $\theta$ with the $x-$axis,as shown in the figure. At four different values of $\theta$,namely $\theta = 8^o, 38^o, 188^o$ and $218^o$,the observed intensities are the same. What is the angle between the direction of polarization and the $x-$axis in degrees?

If a polaroid is kept in the path of uniformly unpolarised light,the ratio of the intensity of the transmitted light to the intensity of the light when the polaroid was not kept in its path is:

Explain the polarization of light by a thin plastic-like sheet.

Three polaroid sheets are co-axially placed as indicated in the diagram. Pass axes of the polaroids $2$ and $3$ make $30^{\circ}$ and $90^{\circ}$ with the pass axis of polaroid sheet $1$. If $I_0$ is the intensity of the incident unpolarised light entering sheet $1$,the intensity of the emergent light through sheet $3$ is

Two polaroids have their polarizing directions parallel so that the intensity of the transmitted light is maximum. The angle through which either polaroid must be turned so that the intensity of the transmitted light is dropped to one-half of the previous transmitted intensity is $.....^\circ$.

Two beams,$A$ and $B$,of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity),a rotation of the polaroid through $30^{\circ}$ makes the two beams appear equally bright. If the initial intensities of the two beams are $I_A$ and $I_B$ respectively,then $\frac{I_A}{I_B} = $