V-Value or normalized frequency is the fundamental relationship between numerical aperture, cut-off wavelength and core radius in step-index fibers.
By definition V=2.405 at the cut-off wavelength of every single-mode fiber waveguide. When the V-Value is greater than 2.405 the fiber will propagate multiple modes. On the contrary, if the V-Value is less than 2.405 then the light propagated through the fiber will be single-mode.
The equation above shows that a high numerical aperture or short cut-off wavelength fibers will dictate a small core radius. This is particularly noticeable for fibers operating in the visible spectrum. It also explains why single mode fibers cannot have large core radius.
Thus it follows that a high numerical aperture dictates a small core, as does a short cut-off wavelength; this is particularly noticeable for fibers operating in the visible spectrum.