Optics... #1

Classical Mechanics Level 5

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 radius of curvature 8 cm and is silvered to make it a concave mirror as shown in the above 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 in figure), the height of the liquid surface in the in the beaker from the apex of the bottom. Consider the paraxial rays only.

A paraxial ray is a ray that makes a small angle to the optical axis of the system, and lies close to the axis throughout the system.

Refractive index of sphere is \(\frac{3}{2}\).

Refractive index of liquid is \(\frac{4}{3}\).

Round that answer to nearest integer.

h is measured in cm

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