  Focusing light through highly scattering materials by modifying the phase
profile of the illuminating beam has attracted a great deal of attention in the
past decade paving the way towards novel applications. Here we discovered a
tradeoff between two seemingly independent quantities of critical importance in
the focusing process: the size of the focal point obtained behind a scattering
medium and the maximum achievable brightness of such focal point. We
theoretically derive and experimentally demonstrate the fundamental limits of
intensity enhancement of the focal point and relate them to the intrinsic
properties of the scattering phenomenon. We demonstrate that the intensity
enhancement limitation becomes dominant when the focusing plane gets closer to
the scattering layer thus limiting the ability to obtain tight focusing at high
contrast, which has direct relevance for the many applications exploring
scattering materials as a platform for high resolution focusing and imaging
