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

Polarized glass is used for sunglasses because...

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.

$A$ mixture of plane polarised and unpolarised light falls normally on a polarizing sheet. On rotating the polarizing sheet about the direction of the incident beam,the transmitted intensity varies by a factor of $4$. Find the ratio of the intensities $I_P$ and $I_0$,respectively of the polarized and unpolarized components in the incident beam.

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):

Three polaroid sheets $P_{1}, P_{2}$ and $P_{3}$ are kept parallel to each other such that the angle between pass axes of $P_{1}$ and $P_{2}$ is $45^{\circ}$ and that between $P_{2}$ and $P_{3}$ is $45^{\circ}$. If an unpolarised beam of light of intensity $128 \ Wm^{-2}$ is incident on $P_{1}$,what is the intensity of light coming out of $P_{3}$?