Re: what is the method of mirror images for calculating electric fields

The method of images is used in analysis of electric fields near conducting 
 materials.

The boundary conditions for electric fields at the interface between a 
conductor and dielectric material demand that there be zero tangential 
component to the electric field at the surface of the conductor.  (If there 
were any tangential field, the free charges in the conductor would be 
pushed around so as to drive the field to zero.  Ergo, there is no 
tangential electric field at the surface of a conductor.)

Because there is no tangential E field at the conductor surface, the 
conductor's surface is an equipotential surface (i.e., conductor surface is 
 at same voltage everywhere). Thus, the E field at a conductor's surface 
will contain only a component normal to the surface.

In the simplest case, this means that in the case of a point charge C 
somewhere above a conducting plane, we can eliminate the conducting plane 
and replace it with a point charge of opposite polarity -C at the mirror 
image location.  The electric field will be identical in both cases.  

Similarly, you can construct images of line charges above a plane, line 
charges near cylinders, point charges near spheres, etc.  You can use the 
image technique for more complicated geometries built of intersecting 
planes using the principle of superposition and recognizing that you must 
account for images of images, ad infinitum, until sufficient accuracy is 
reached (i.e., any remaining image charges are too far away to be of 
significant influence).  

Note that conformal mapping techniques may also be useful in transforming a 
given geometry into a more readily analyzable geometry, with appropriate 
transformation of the result back into the original coordinate frame.

The technique is also useful in dynamic situations, such as analyzing the 
performance of antennas near conducting ground planes.  The ground plane 
can be eliminated and replaced with the mirror image of the antenna 
radiating a signal 180 degrees out of phase.

This topic of images is covered in most intermediate-level texts on 
electrogmagnetic field theory and application.

See, for example, 

Ramo, Whinnery, and VanDuzer, "Fields and Waves in Communication 
Electronics", Wiley, 1965, pp. 97-100. 

Steve Czarnecki