A human lens and cornea act as a bi-convex thin lens in the eye with an average index of refraction of 1.15. The LASIK operation (laser-assisted in situ keratomileusis) re-shapes the front of the cornea to correct for both near-sightedness (myopia) and far-sightedness (hyperopia), as well as astigmatisms. A doctor needs to correct the vision of a person who can't see objects any closer than 50 cm by shaving thin slivers off the cornea to either increase or decrease the radius of curvature, while maintaining the spherical shape. If the retina in a typical eye is 24 mm behind the axis of the lens-cornea system, and the rear surface of the lens has a radius of curvature of 6.33 mm, what is the necessary change in the radius of curvature for the surface of the cornea?
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