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

The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by the light of wavelength $6000 \mathop A\limits^o$. If the slit is illuminated by light of another wavelength, the angular separation decreases by $20 \%$. The wavelength of light used is