Two wavelengths $$\lambda_1$$ and $$\lambda_2$$ are used in Young's double slit experiment. $$\lambda_1=450 \mathrm{~nm}$$ and $$\lambda_2=650 \mathrm{~nm}$$. The minimum order of fringe produced by $$\lambda_2$$ which overlaps with the fringe produced by $$\lambda_1$$ is $$n$$. The value of $$n$$ is _______.

Two waves of intensity ratio $$1: 9$$ cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is $$I_1$$ (b) Waves are coherent is $$I_2$$ and differ in phase by $$60^{\circ}$$. If $$\frac{I_1}{I_2}=\frac{10}{x}$$ then $$x=$$ _________.

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 _________ $$\times 10^{-4} \mathrm{~m}$$.