In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab as 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 20 divisions on vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is $$\frac{x}{10}\times10^{-3}$$, where $$x$$ is ___________

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, $$\mu_r=1$$)

As shown in the figure, three identical polaroids P$$_1$$, P$$_2$$ and P$$_3$$ are placed one after another. The pass axis of P$$_2$$ and P$$_3$$ are inclined at angle of 60$$^\circ$$ and 90$$^\circ$$ with respect to axis of P$$_1$$. The source S has an intensity of 256 $$\frac{W}{m^2}$$. The intensity of light at point O is ____________ $$\frac{W}{m^2}$$.

An object is placed on the principal axis of convex lens of focal length 10cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5cm inside the mirror. The distance of the object from the lens is ___________ cm.