1) A thin lens is one where the thickness is much less than the radii of curvature on the two surfaces. Light rays are considered to bend at the center of such a lens.
2) The thin lens equation relates the focal length of a lens to its radii of curvature and refractive index. Refractive power is defined as the change in refraction caused by a lens.
3) Back vertex power and front vertex power are defined based on the reduced distance from poles of the lens to focal points, accounting for the refractive index. The true power of a lens is its equivalent power based on the equivalent focal length.