The intensity of transmitted light when a polaroid sheet is placed between two crossed polaroids at $22.5^{\circ}$ from the polarization axis of one of the polaroids is (where $I_0$ is the intensity of polarized light after passing through the first polaroid):

In the visible region of the spectrum,the rotation of the plane of polarization is given by $\theta = a + \frac{b}{\lambda^2}$. The optical rotation produced by a particular material is found to be $30^\circ$ per mm at $\lambda = 5000 \ \mathring{A}$ and $50^\circ$ per mm at $\lambda = 4000 \ \mathring{A}$. The value of constant $a$ will be:

The angle between a polarizer and an analyzer is $60^o$. If light with an amplitude $A$ is incident on the polarizer,what is the amplitude of the light emerging from the analyzer?

Unpolarised light of intensity $I_0$ is incident on a polarizer. What is the percentage of the intensity of light that gets transmitted from the polarizer (in $\%$)?

Indicate the signals used for unpolarised,polarised,and partially polarised light.

$A$ $20 \ cm$ 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