It depends on the type of grass you have. If you have St Augustine, mow it at 4 inches and that will be shade enough. If you have zoysia, mow it at 1 1/2 to 2 inches, no longer. Zoysia has many problems that aren't necessarily related to too much sun or shade. I am attaching a link that will help if you have zoysia.
http://edis.ifas.ufl.edu/pdffiles/LH/LH01100.pdf