Daddy Long Legs (1955)

On a trip to France, millionaire Jervis Pendelton sees an 18 year old girl in an orphanage. Enchanted with her, but mindful of the difference in their ages, he sponsors her to college in New England. She writes him letters, which he doesn't read. After 3 years, he goes to visit her at a dance, not telling her that he is her benefactor. They fall in love, but the usual movie-type difficulties get in the way before they can get together at the end.