Three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $P_2$ and $\mathrm{P}_3$ are inclined at an angle of $60^{\circ}$ and $90^{\circ}$ with respect to axis of $\mathrm{P}_1$. The source has an intensity $256 \mathrm{~W} / \mathrm{m}^2$. The intensity of light at point ' O ' is $\left(\cos 30^{\circ}=\sqrt{3} / 2, \cos 60^{\circ}=0.5\right)$

In a single slit diffraction experiment, for a wavelength of light ' $\lambda$ ', half-angular width of the principle maxima is ' $\theta$ '. Also for wavelength of light $\mathrm{p} \lambda$, the half angular width of the principle maxima is $q \theta$. The ratio of the halfangular widths of the first secondary maxima in the first case to second case will be

In a double slit experiment, the distance between slits is increased 10 times, whereas their distance from screen is halved, the fringe width