  Using the electrostatic approximation, we analyze electromagnetic fields
scattered by sharp conical metal tips, which are illuminated with light
polarized along the tip axis. We establish scaling relations for the scattered
field amplitude and phase, whose validity is verified with numerical
simulations. Analytic expressions for the wavelength, at which the scattered
field near the tip changes its direction, and field decay near the tip
extremity are obtained, relating these characteristics to the cone angle and
metal permittivity. The results obtained have important implications to various
tip-enhanced phenomena, ranging from Raman and scattering near-field imaging to
photoemission spectroscopy and nano-optical trapping.
