a transparent sphee of radius R and refractive index u is kept in air.At what distance from the surface of sphere should a point object be placed so as to form a real image at same distance from sphere?

Inorder to get a real image at same distance from sphere we should place the object at 2f on the principal axis.    We can calculate the distance using Lens maker’s equation: 1/f=(n-1)[1/r-1/R+(n-1)d/nrR]                                   where, f=focal length   ,n=refractive index   ,r=radius of curvature of the lens surface nearest to light ray   ,           R=radius of  curvature of the lens surface farthest to light ray    ,d=diameter of sphere.                       In a sphere r=R  ,   so using  your  values we get                                                                                                                                1/f=(u-1)[1/R-1/R +(u-1)d/u*R^2                                                                                                                  1/f=(u-1)[1+(u-1)d/uR^2]

                                               1/f=(u-1)[(uR^2+du-d)/uR^2]

                                               1/f=(u^2R^2+du^2-du-uR^2-du-d)/uR^2

                                                f=nR^2/u^2R^2- du^2- 2du- uR^2-d

                                                f=R^2/3R^2-du-3d

                                   then 2f=R^2/6R^2-2du-6d