'n' polarizing sheets are arranged such that each makes an angle $45^\circ$ with the preceding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $I/64$. The value of $n$ will be

Two polaroids $A$ and $B$ are placed perpendicularly in the path of a beam of unpolarized light. In between these two,a third polaroid $C$ is placed at an angle of $30^o$ with that of $A$. The percentage of intensity of incident unpolarized light that emerges from $B$ is ........$\%$.

An unpolarized beam of intensity $2a^2$ passes through a thin polaroid. Assuming zero absorption in the polaroid,the intensity of emergent plane-polarized light is

Show that when unpolarized light passes through a polarizer,the intensity of the emerging light is half that of the intensity of the incident light.

Two polaroids are oriented with their planes perpendicular to incident light and transmission axis making an angle $30^{\circ}$ with each other. What fraction of incident unpolarised light is transmitted (in $\%$)? $(\cos 30^{\circ} = \sqrt{3} / 2)$

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at $30^\circ$ and $90^\circ$, respectively, with respect to the horizontal axis. $A$ third polarizer with its transmission axis at $60^\circ$ with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is . . . . . . .