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 ____________.

In the given figure, the face $$A C$$ of the equilateral prism is immersed in a liquid of refractive index '$$n$$'. For incident angle $$60^{\circ}$$ at the side $$A C$$, the refractive light beam just grazes along face $$A C$$. The refractive index of the liquid $$n=\frac{\sqrt{x}}{4}$$. The value of $$x$$ is ____________.

(Given refractive index of glass $$=1.5$$ )