Soul Man is a 1986 American comedy film about a white man who takes tanning pills in order to pretend to be black and qualify for a black-only scholarship at Harvard Law School. The film was directed by Steve Miner and stars C. Thomas Howell, Rae Dawn Chong, Arye Gross, James Earl Jones, Leslie Nielsen, James B. Sikking, and Julia Louis-Dreyfus.
I also appreciate the contrast put in here with respect to Tootsie, which has a similar plot structure.