The relation $I = I_0 \cos^2 \theta$ is known as (where $I_0$ is the intensity of incident light on the analyser,$I$ is the intensity of emergent light from the analyser,and $\theta$ is the angle between the plane of polarization and the axis of the analyser):

$A$ $20 \ cm$ 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

Three polaroid sheets are kept parallel to each other such that the first and the last are crossed. Unpolarised light of intensity $32 \ W m^{-2}$ falls normally on the first sheet and passes through all the polaroid sheets. If the intensity of the emerging light from the third sheet is $3 \ W m^{-2}$,then the angle between the axes of the first two polaroid sheets is: (in $^{\circ}$)

Two polarizers are oriented with their principal planes making an angle of $60^{\circ}$ with each other. The percentage of incident unpolarized light which passes through the system is: (in $\%$)

An unpolarised beam of intensity $I_{0}$ falls on a polaroid. The intensity of the emergent light is

$A$ system of three polarizers $P_1, P_2, P_3$ is set up such that the pass axis of $P_3$ is crossed with respect to that of $P_1$. The pass axis of $P_2$ is inclined at $60^{\circ}$ to the pass axis of $P_3$. When a beam of unpolarized light of intensity $I_0$ is incident on $P_1$,the intensity of light transmitted by the three polarizers is $I$. The ratio $(I_0/I)$ equals (nearly)