The X-Y plane be taken as the boundary between two transparent media $$\mathrm{M}_{1}$$ and $$\mathrm{M}_{2}$$. $$\mathrm{M}_{1}$$ in $$Z \geqslant 0$$ has a refractive index of $$\sqrt{2}$$ and $$M_{2}$$ with $$Z<0$$ has a refractive index of $$\sqrt{3}$$. A ray of light travelling in $$\mathrm{M}_{1}$$ along the direction given by the vector $$\overrightarrow{\mathrm{P}}=4 \sqrt{3} \hat{i}-3 \sqrt{3} \hat{j}-5 \hat{k}$$, is incident on the plane of separation. The value of difference between the angle of incident in $$\mathrm{M}_{1}$$ and the angle of refraction in $$\mathrm{M}_{2}$$ will be __________ degree.

An object 'O' is placed at a distance of $$100 \mathrm{~cm}$$ in front of a concave mirror of radius of curvature $$200 \mathrm{~cm}$$ as shown in the figure. The object starts moving towards the mirror at a speed $$2 \mathrm{~cm} / \mathrm{s}$$. The position of the image from the mirror after $$10 \mathrm{~s}$$ will be at _________ $$\mathrm{cm}$$.

In an experiment with a convex lens, The plot of the image distance $$\left(v^{\prime}\right)$$ against the object distance ($$\left.\mu^{\prime}\right)$$ measured from the focus gives a curve $$v^{\prime} \mu^{\prime}=225$$. If all the distances are measured in $$\mathrm{cm}$$. The magnitude of the focal length of the lens is ___________ cm.

A thin prism of angle $$6^{\circ}$$ and refractive index for yellow light $$\left(\mathrm{n}_{\mathrm{Y}}\right) 1.5$$ is combined with another prism of angle $$5^{\circ}$$ and $$\mathrm{n}_{\mathrm{Y}}=1.55$$. The combination produces no dispersion. The net average deviation $$(\delta)$$ produced by the combination is $$\left(\frac{1}{x}\right)^{\circ}$$. The value of $$x$$ is ____________.