'$$n$$' polarizing sheets are arranged such that each makes an angle $$45^{\circ}$$ with the preceeding 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:

Two polaroide $$\mathrm{A}$$ and $$\mathrm{B}$$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid $$\mathrm{C}$$ is placed between $$\mathrm{A}$$ and $$\mathrm{B}$$ bisecting angle between them. If intensity of unpolarized light is $$\mathrm{I}_{0}$$ then intensity of transmitted light after passing through polaroid $$\mathrm{B}$$ will be:

A thin prism $P_1$ with an angle $6^{\circ}$ and made of glass of refractive index $1.54$ is combined with another prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without average deviation. The angle of prism $P_2$ is