This paper presents a method for recovering the reflectance and shape of a surface from a single hyper spectral image. To do this, we depart from a reflectance model based on a physical interpretation of the reflection process where the geometry of the scene and the properties of the object surface describe the image formation process. With the model in hand, we propose a solution to the recovery of the reflection parameters via an optimisation approach that aims at recovering both the surface normals and the reflectance. This, in turn, allows for the application of the method by Frankot and Chellappa [8] so as to recover the surface depth at each pixel. We demonstrate the utility of our method for the recovery of both reflectance and surface depth on synthetic and real world images.