$A$ 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:

Two polarizers are placed such that the angle between their transmission axes is $60^o$. If unpolarised light of intensity $I_0$ is incident on the first polarizer,then the transmitted intensity from the second polarizer will be

$V_o$ 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:

The pass-axes of two polarisers were kept such that the incident unpolarised beam of intensity $I_0$ gets completely blocked. Another polariser was introduced in between these two polarisers with its pass-axis at $60^{\circ}$ with respect to the pass-axis of the first one. The output intensity would then become

Statement-$1$: The blue part of the sky is clearly visible through a calcite crystal. The intensity of the transmitted light changes as the crystal is rotated.
Statement-$2$: Light from the sky is due to the scattering of sunlight by particles in the atmosphere.

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 $P_{3}$?