In a single slit diffraction pattern, a light of wavelength 6000$$\mathop A\limits^o$$ is used. The distance between the first and third minima in the diffraction pattern is found to be $$3 \mathrm{~mm}$$ when the screen in placed $$50 \mathrm{~cm}$$ away from slits. The width of the slit is _________ $$\times 10^{-4} \mathrm{~m}$$.

In a double slit experiment shown in figure, when light of wavelength $$400 \mathrm{~nm}$$ is used, dark fringe is observed at $$P$$. If $$\mathrm{D}=0.2 \mathrm{~m}$$, the minimum distance between the slits $$S_1$$ and $$S_2$$ is _________ $$\mathrm{mm}$$.

A parallel beam of monochromatic light of wavelength 5000 $$\mathop A\limits^o$$ is incident normally on a single narrow slit of width $$0.001 \mathrm{~mm}$$. The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of _________ (degree).

Unpolarised light of intensity 32 Wm$$^{-2}$$ passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is 3 Wm$$^{-2}$$, then the angle between pass axis of first two polaroids is ______________ $$^\circ$$.