Geometrical OpticsMedium

Question

A transparent and homogeneous sphere of glass of radius r is immersed in water (refractive indices of glass and water being aμg = 3/2 and aμw = 4/3). The image of a point object O, located at distance d on its axis in front of the sphere, is formed at point I at the same distance d from the sphere on the opposite side as shown.

The distance d is equal to

Options

A.2r
B.3r
C.6r
D.8r

Solution

[Key Concept: Refraction at a spherical surface: μ2/v − μ1/u = (μ2 − μ1)/R; a symmetric object-image pair makes the ray inside the sphere parallel to the axis.]

$\begin{matrix} & \frac{\mu_{r}}{v} - \frac{u_{i}}{v} = \frac{\mu_{r} - \mu_{i}}{R} \\ & \frac{3}{2(\infty)} - \frac{4}{3( - d)} = \frac{\frac{3}{2} - \frac{4}{3}}{r} \\ & \frac{4}{3d} = \frac{1}{6r} \\ & d = 8r \end{matrix}\ \ \ $

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