'$$n$$' 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:

In a Young's double slit experiment, two slits are illuminated with a light of wavelength $$800 \mathrm{~nm}$$. The line joining $$A_{1} P$$ is perpendicular to $$A_{1} A_{2}$$ as shown in the figure. If the first minimum is detected at $$P$$, the value of slits separation 'a' will be:

The distance of screen from slits D = 5 cm

In Young's double slits experiment, the position of 5$$\mathrm{^{th}}$$ bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and wavelength of used monochromatic light is 600 nm. The separation between the slits is :