$A$ $300 \, mm$ long tube contains $60 \, cm^3$ of a concentrated sugar solution. When placed in a polarimeter,it produces an optical rotation of $10^\circ$. If the specific rotation of sugar is $60^\circ$,calculate the amount of sugar in grams present in the tube.

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):

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 .......... $\text{ Lumens}$.

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):

After passing through a polariser,a linearly polarised light of intensity $I$ is incident on an analyser making an angle of $30^{\circ}$ with that of the polariser. The intensity of light emitted from the analyser will be

$A$ polaroid $(I)$ is placed in front of a monochromatic source. Another polaroid $(II)$ is placed in front of this polaroid $(I)$ and rotated until no light passes. $A$ third polaroid $(III)$ is now placed in between $(I)$ and $(II)$. In this case,will light emerge from $(II)$? Explain.