We introduce a method of recovering the shape of a smooth dielectric object using diffuse polarization images taken with different directional light sources. We present two constraints on shading and polarization and use both in a single optimization scheme. This integration is motivated by photometric stereo and polarization-based methods having complementary abilities. Polarization gives strong cues for the surface orientation and refractive index, which are independent of the light direction. However, employing polarization leads to ambiguities in selecting between two ambiguous choices of the surface orientation, in the relationship between the refractive index and zenith angle (observing angle). Moreover, polarization-based methods for surface points with small zenith angles perform poorly owing to the weak polarization. In contrast, the photometric stereo method with multiple light sources disambiguates the surface normals and gives a strong relationship between surface normals and light directions. However, the method has limited performance for large zenith angles and refractive index estimation and faces strong ambiguity when light directions are unknown. Taking the advantages of these methods, our proposed method recovers surface normals for small and large zenith angles, light directions, and refractive indexes of the object. The proposed method is positively evaluated in simulations and real-world experiments.