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

Two polaroids are placed in the path of an unpolarised light beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid,whose polarisation axis makes an angle $\theta$ with that of the first polaroid,is placed between the polaroids,then the intensity of light emerging from the last polaroid is

$A$ mixture of plane-polarized and unpolarized light falls normally on a polarizing sheet. On rotating the polarizing sheet about the direction of the incident beam,we find that the ratio of maximum to minimum transmitted intensity is $4$. Find the ratio of the intensities $I_P$ and $I_0$,respectively,of the polarized and unpolarized components in the incident beam.

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:

$A$ calcite crystal is placed over a dot on a piece of paper and rotated. On seeing through the calcite,one will see:

Two polaroids are placed in the path of an unpolarised beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid,whose polarisation axis makes an angle $\theta$ with the polarisation axis of the first polaroid,is placed between these polaroids,then the intensity of light emerging from the last polaroid will be: