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# A parallel beam of light is incident on a solid transparent sphere of refractive inbox $\mu$. If a point image is formed on the back of the sphere , the refractive index of sphere is

$(a)\;3 \\ (b)\;2 \\ (c)\;1.5 \\ (d)\;2.5$

Sphere is considered as a solid transparent with two
Spherical refractive surface of radius of curvature $r_1=r_2=r$
The image is formed at $2r$ distance from the pole of the 1st surface and so no refraction takes place in the second surface.
effectively refraction takes place in single surface and image is formed inside the refractive medium.
$\therefore \large\frac{n_1}{u} +\frac{n_2}{v} =\large\frac{n_2 -n_1}{r}$
$n_1$- refractive index of air
$n_2$ - refractive index of medium $=\mu$
$u=\infty$
$v= 2r$
$\large\frac{1}{\infty}+\frac{\mu}{2r}=\frac{(\mu-1)}{r}$
$\mu =2 \mu -2$
$\mu=2$
Hence b is the correct answer.