$A$ beam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $45^{\circ}$ relative to that of $A$. The intensity of emergent light is:

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:

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of the light beam emerging from the analyzer is measured as $100 \text{ Lumens}$. Now,if the analyzer is rotated around the horizontal axis (direction of light) by $30^{\circ}$ in the clockwise direction,the intensity of the emerging light will be .......... $\text{ Lumens}$.

When unpolarized light of intensity $I_0$ is incident on a polarizing sheet,the intensity of light that does not pass through is:

An unpolarised beam of light is incident on a group of three polarising sheets arranged such that the angle between the axes of any two adjacent sheets is $30^{\circ}$. The ratio of the intensities of polarised light emerging from the second and third sheets is