The figure ,shows a transparent sphere of radius`R`and refractive index`mu`.An object `O`is placed at a distance `x` from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface.
if an object is Placed at a distance`R` from the pole of first surface ,then the real image is formed at a distance `R`from thepole of the second surface.The refractive index`mu` of the spher is given by

Options

A. `1.5`
B. `2`
C. `sqrt(2)`
D. None of these

Answer

B

Explanation

From the symmetry of the fig.ray inside the sphere is parallel to principal axis.Taking refraction at`A`
`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R )`
`(mu)/(oo)-(1)/(-R)=(mu-1)/(R )`
`(1)/(R )=(mu-1)/(R ) rArr mu-1=1`
`mu=2`