Unpolarized light of intensity $I$ passes through an ideal polarizer $A$. Another identical polarizer $B$ is placed behind $A$. The intensity of light beyond $B$ is found to be $\frac{I}{2}$. Now,another identical polarizer $C$ is placed between $A$ and $B$. The intensity beyond $B$ is now found to be $\frac{I}{8}$. The angle between polarizer $A$ and $C$ is: ......$^{\circ}$

An optically active compound:

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 $3$? $(\cos 30^{\circ}=\sqrt{3} / 2, \cos 90^{\circ}=0, \cos 60^{\circ}=1 / 2)$

Three polaroid sheets $P_{1}, P_{2}$ and $P_{3}$ are kept parallel to each other such that the angle between pass axes of $P_{1}$ and $P_{2}$ is $45^{\circ}$ and that between $P_{2}$ and $P_{3}$ is $45^{\circ}$. If an unpolarised beam of light of intensity $128 \ Wm^{-2}$ is incident on $P_{1}$,what is the intensity of light coming out of $P_{3}$?

The transverse nature of light is shown by

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} = $