Question

What would the strength be if we cut a lens in half?

Answer 1

The combined strength of the two lenses will stay the same.

That is, if the cut is so thin that we can neglect it (no loss of material), and if the halves stay close together

Strength is `1/f` (`f` in meters)

So `1/f =1/(f_1) +1/f_2`

If your original lens were symmetrical (bi-convex or bi-concave), so that each half would be the same, then each half would have half the strength, and thus twice the focal length of the original lens.