$A$ polaroid is placed at $45^{\circ}$ to an incoming linearly polarized light of intensity $I_0$. The intensity of light passing through the polaroid after polarization will be:

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.....$^o$

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.

$A$ beam of natural light falls on a system of $5$ polaroids,which are arranged in succession such that the pass axis of each polaroid is turned through $60^{\circ}$ with respect to the preceding one. The fraction of the intensity of incident light that passes through the system is:

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} = $

As shown in the figure,three identical polaroids $P_1$,$P_2$,and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclined at angles of $60^{\circ}$ and $90^{\circ}$ with respect to the axis of $P_1$. The source $S$ has an intensity of $256 \text{ W/m}^2$. The intensity of light at point $O$ is $........... \text{ W/m}^2$.