Final answer:
The film that portrays Nightingale's persistence and confrontation with medicine in the 1930s is 'The Lamp'. It showcases a nurse challenging traditional medical practices.
Step-by-step explanation:
The 1930s film that clearly portrayed Nightingale's persistence and head-to-head confrontation with medicine is The Lamp.
This film tells the story of a determined nurse who challenges the traditional medical practices of the time. Through her unwavering dedication to patient care and her ability to stand up against the male-dominated medical establishment, she showcases Nightingale's qualities of persistence and strength.