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(C) The refraction formula at a spherical surface is given by $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,the light travels fro

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$6$

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(C) The refraction formula at a spherical surface is given by $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,the light travels from glass $(\mu_1 = 1.5)$ to air $(\mu_2 = 1.0)$.The object is at the center,so the distance $u = -6 \ cm$.The radius of curvature $R = -6 \ cm$ (since the center of curvature is to the left of the surface).Substituting these values: $\frac{1.0}{v} - \frac{1.5}{-6} = \frac{1.0 - 1.5}{-6}$.$\frac{1}{v} + \frac{1.5}{6} = \frac{-0.5}{-6}$.$\frac{1}{v} + 0.25 = \frac{0.5}{6}$.$\frac{1}{v} = \frac{1}{12} - \frac{1}{4} = \frac{1 - 3}{12} = -\frac{2}{12} = -\frac{1}{6}$.Thus,$v = -6 \ cm$.The negative sign indicates that the image is virtual and formed on the same side as the object,at a distance of $6 \ cm$ from the surface.

$A$ point object is placed at the center of a glass sphere of radius $6 \ cm$ and refractive index $1.5$. The distance of the virtual image from the surface of the sphere is.......$cm$

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