A transparent solid sphere of radius 2 cm and density $\rho$ floats in a transparent liquid of density 2$\rho$  kept in a beaker. The bottom of the beaker is spherical in shape with its radius of curvature 8 cm and is silvered to make it a concave mirror as shown in Fig. When an object is placed at a distance of 10 cm directly above the centre of the sphere its final image coincides with it. If ‘h’ is the height of liquid surface from the apex of the bottom as shown in figure. Consider paraxial rays only for image formation. The refractive index of the sphere is $\frac{3}{2}$ and that of the liquid is $\frac{4}{3}$ .

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