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 $$=1.5$$ )

The graph between $$\frac{1}{u}$$ and $$\frac{1}{v}$$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is $$1.5$$ and its both the surfaces have same radius of curvature $$R$$. The value of $$R$$ will be ____________ $$\mathrm{cm} .$$ (where $$u=$$ object distance, $$v=$$ image distance)

A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is ____________ cm.