$A$ 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.

In the figure,suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also,let the center disk be rotated on the common axis with an angular speed $\omega$. If unpolarized light is incident on the left disk with an intensity $I_{max}$,the intensity of the beam emerging from the right disk is given by:

$A$ $20 \ cm$ length of a certain solution causes right-handed rotation of $38^{\circ}$. $A$ $30 \ cm$ length of another solution causes left-handed rotation of $24^{\circ}$. The optical rotation caused by a $30 \ cm$ length of a mixture of the above solutions in the volume ratio $1:2$ is

$A$ light beam has an amplitude $A$,and the angle between the analyser and the polariser is $60^o$. What is the amplitude of the light reflected by the analyser?

The phenomenon of polarization shows that light has ......... nature.

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