The Blue Lagoon (1980)
The Blue Lagoon is a 1980 American romantic adventure film directed by Randal Kleiser. The screenplay by Douglas Day Stewart was based on the novel The Blue Lagoon by Henry De Vere Stacpoole. The film stars Brooke Shields and Christopher Atkins. The original music score was composed by Basil Poledouris and the cinematography was by Néstor Almendros. The film is a remake of a 1949 film by the same name.
More at Wikipedia.