Two nicols are crossed to each other. Now one of them is rotated through $60^{\circ}$. What percentage of incident light will pass through the system (in $\%$)?

Three polarising sheets are placed co-axially. The pass axes of polaroids $2$ and $3$ make angles of $30^{\circ}$ and $90^{\circ}$ respectively with the pass axis of polaroid $1$. If $I_0$ is the intensity of unpolarised light entering sheet $1$,what is the intensity of the light emerging from sheet $3$? $(\cos 30^{\circ}=\sqrt{3} / 2, \cos 90^{\circ}=0, \cos 60^{\circ}=1 / 2)$

$A$ mixture of plane polarised and unpolarised light falls normally on a polarizing sheet. On rotating the polarizing sheet about the direction of the incident beam,the transmitted intensity varies by a factor of $4$. Find the ratio of the intensities $I_P$ and $I_0$,respectively of the polarized and unpolarized components in the incident beam.

An unpolarised beam of intensity $I_{0}$ falls on a polaroid. The intensity of the emergent 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 have their polarizing directions parallel so that the intensity of a transmitted light is maximum. The angle through which either polaroid must be turned if the intensity is to drop by one-half is.....$^o$