'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

$A$ 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 the emergent light is

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

When a polaroid sheet is rotated between two crossed polaroids,then the transmitted light intensity will be maximum for a rotation of: (in $^{\circ}$)

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:

$A$ $300 \, mm$ long tube contains $60 \, cm^3$ of a concentrated sugar solution. When placed in a polarimeter,it produces an optical rotation of $10^\circ$. If the specific rotation of sugar is $60^\circ$,calculate the amount of sugar in grams present in the tube.