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 $\frac{I_{1}+I_{2}}{I_{0}}=$ __________.

In Young's double slit experiment, two slits $$S_{1}$$ and $$S_{2}$$ are '$$d$$' distance apart and the separation from slits to screen is $$\mathrm{D}$$ (as shown in figure). Now if two transparent slabs of equal thickness $$0.1 \mathrm{~mm}$$ but refractive index $$1.51$$ and $$1.55$$ are introduced in the path of beam $$(\lambda=4000$$ $$\mathop A\limits^o $$) from $$\mathrm{S}_{1}$$ and $$\mathrm{S}_{2}$$ respectively. The central bright fringe spot will shift by ___________ number of fringes.

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium $$-1$$) and 6.8 (medium $$-2$$), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be $${\tan ^{ - 1}}{\left( {1 + {{10} \over \theta }} \right)^{{1 \over 2}}}$$ the value of $$\theta$$ is __________.

(Given for dielectric media, $$\mu_r=1$$)