An unpolarised beam of light of intensity $I_0$ passes through two linear polarisers making an angle of $30^{\circ}$ with respect to each other. The emergent beam will have an intensity:

In a system of two crossed polarisers,it is found that the intensity of light from the second polariser is half of that from the first polariser. The angle between their pass axes is (in $^{\circ}$)

Through which characteristic can we distinguish light waves from sound waves?

How can it be determined whether a given light is unpolarized,plane-polarized,or partially plane-polarized?

Which of the following phenomena can be demonstrated by light,but not with sound waves in an air column?

$A$ cylindrical tube of length $0.2 \,m$ and radius $R$ with sugar solution of concentration $C$ produces a rotation of $\theta$ in the plane of vibration of a plane-polarized light. The same sugar solution is transferred to another tube of length $0.3 \,m$ of the same radius. The remaining gap is filled by distilled water. Now, the optical rotation produced is: