A photographic camera uses a thin convex lens of focal length 5.0cm. The film is positioned 5.20cm behind the lens.
(a) Determine the range of object distances that can be sharply focused on the film without moving the film itself if the lens can be moved forward or backward by at most 1.0cm from its initial position.
(b) A person standing 3.0m away is to be photographed. Calculate the precise shift required in the lens position to obtain a sharp image on the film and state the direction of the shift (towards or away from the film).
(c) Explain briefly why the depth of field (the range found in part (a)) depends on both the focal length of the lens and the permissible lens movement.