Answer
See answer.
It is not possible for a lens to have a positive f for some colors and negative f for others.
Work Step by Step
The angle by which light is bent as it enters the glass depends on the material’s index of refraction, n. Because n depends on wavelength, different colors are bent by different amounts and will converge at slightly different points.
It is not possible for a lens to have a positive f for some colors and negative f for others. The lensmaker’s equation shows that for a lens of a given shape, the focal length has the same sign, as long as n is greater than 1. The index of refraction varies slightly for different colors, but n-1 is always positive.
On physical grounds, light of different colors bend by different amounts as they enter or leave the glass, but nevertheless, the rays all bend toward the normal or away from the normal, respectively. The rays will either all converge, or all diverge.