Sea ice plays a critical role in the climate system through its albedo, which constrains light transmission into the upper ocean. In spring and summer, light transmission through sea ice is influenced by its iconic blue melt ponds, which significantly reduce surface albedo. We show that the geometry of surface melt ponds plays an important role in the partitioning of instantaneous solar radiation under sea ice by modeling the three-dimensional light field under ponded sea ice. We find that aggregate properties of the instantaneous sub-ice light field, such as the enhancement of available solar energy under bare ice regions, can be described using a new parameter closely related to pond fractal geometry. We then explore the influence of pond geometry on the ecological and thermodynamic sea-ice processes that depend on solar radiation.