Scattering of light is considered a nuisance in microscopy. It limits the penetration depth and strongly deteriorates the achievable resolution. However, by gaining active spatial control over the optical wave front it is possible to manipulate the propagation of scattered light far in the multiple scattering regime. These wave front shaping techniques have given rise to new high-resolution microscopy methods based on strong light scattering. This is based on the realization that scattering by stationary particles performs a linear transformation on the incident light modes. By inverting this linear transformation, one can focus light through an opaque material and even inside it. An extremely high resolution focus can be obtained using scatterers embedded in a high-index medium, where the diffraction limit for focusing is reduced by a factor n. We have constructed a scattering lens made of the high-index material gallium phosphide (GaP) which is transparent over most of the visible spectrum and has the highest index of all nonabsorbing materials in the visible range. This yields a focal spot resolution of less than 100 nm, and it seems theoretically possible to create a focus of order 70 nm. The system resolution of a microscope based on this lens could be substantially higher.n© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.