$A$ plane polarized light is incident normally on a tourmaline plate. Its $\vec{E}$ vectors make an angle of $60^{\circ}$ with the optic axis of the plate. Find the percentage difference between initial and final intensities. (in $\%$)

Statement-$I$: On viewing the clear blue portion of the sky through a calcite crystal,the intensity of transmitted light varies as the crystal is rotated.
Statement-$II$: The light coming from the sky is polarized due to the scattering of sunlight by particles in the atmosphere. The scattering is largest for blue light.

Which of the following is a biaxial crystal?

$V_o$ and $V_E$ represent the velocities,$\mu_o$ and $\mu_E$ represent the refractive indices of ordinary and extraordinary rays for a doubly refracting crystal. Then:

$A$ 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:

'n' polarizing sheets are arranged such that each makes an angle $45^\circ$ with the preceding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $I/64$. The value of $n$ will be