A beam of light consisting of two wavelengths $$7000~\mathop A\limits^o $$ and $$5500~\mathop A\limits^o $$ is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is $$2.5 \mathrm{~mm}$$ and the distance between the plane of slits and the screen is $$150 \mathrm{~cm}$$. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is $$n \times 10^{-5} \mathrm{~m}$$. The value of $$n$$ is __________.

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $$t=10 \mu \mathrm{m}$$ and refractive index $$\mu=1.2$$ is inserted infront of slit $$S_{1}$$. The experiment is conducted in air $$(\mu=1)$$ and uses a monochromatic light of wavelength $$\lambda=500 \mathrm{~nm}$$. Due to the insertion of the plate, central maxima is shifted by a distance of $$x \beta_{0} . \beta_{0}$$ is the fringe-width befor the insertion of the plate. The value of the $$x$$ is _____________.

In a Young's double slit experiment, the intensities at two points, for the path differences $\frac{\lambda}{4}$ and $\frac{\lambda}{3}$ ( $\lambda$ being the wavelength of light used) are $I_{1}$ and $I_{2}$ respectively. If $I_{0}$ denotes the intensity produced by each one of the individual slits, then $\frac{I_{1}+I_{2}}{I_{0}}=$ __________.