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A transparent solid sphere of radius 2 c...

A transparent solid sphere of radius `2 cm` and density `rho` floats in a transparent liquid of density `2rho` kept in a beaker. The bottom of the beaker is spherical in shape with radius of curvature `8 cm` and is silvered to make it concave mirror as shown in the figure. When an object is placed at a distance of `10 cm` directly above the centre of the sphere C, its final image coincides with it. Find h (as shown in the figure ), the height of the liquid surface in the beaker from the apex of the bottom. Consider the paraxial rays only. The refractive index of the sphere is `3//2` and that of the liquid is `4//3.`

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The correct Answer is:
15 cm
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