The electromagnetic field scattered from an inhomogeneous dielectric slab is calculated by both approximate and exact methods. A novel approximate inverse solution is found, enabling the size and strength of the inhomogeneity to be determined. Examples of scattering from objects of variable size and strength are presented with corresponding quantitative inverse solutions. When applied to exact forward data, the inversion algorithm quantitatively reconstructs the parameters to an accuracy within 20%, even when applied outside the range of validity of the approximate solution. A comparison is made with a reconstruction based upon the first Born approximation which is found to be neither qualitatively nor quantitatively accurate.