Optical field at the center of a sphere

The paper gives an exact formula for determining the intensity of an optical field at the center of a spherical particle of arbitrary radius obtained by evaluating an indeterminate form of the 0/0 type of Mie theory for the electric-field components at the center of the sphere. This formula is valid for arbitrary values of the complex refractive index of the particle material and arbitrary wavelengths of the incident radiation. An approximation for large particles and two approximations for particle sizes less than 10$^{-4}$ cm are obtained. The solution obtained for the optical-field intensity at the center of small particles coincides with the classical Lorentz formula for local fields.