What is the relationship between focal length and the distance to the film when the lens is focused at infinity?

When a lens is focused at infinity, the relationship between focal length and the distance to the film (or sensor) is characterized by the equation of a thin lens. In this situation, the focal length of the lens is equivalent to the distance between the lens and the film or sensor. When focusing on distant objects, the rays of light coming from those objects are essentially parallel by the time they reach the lens, and thus they converge at a point that is located at the focal length of the lens.

This means that, when the lens is properly focused at an infinite distance, the sensor or film must be positioned precisely at the focal length of the lens. Therefore, the focal length and the distance to the film remain the same when the lens is set to focus at infinity. Understanding this relationship is crucial for achieving accurate focus in photography and other optics-related fields.