A digital camera has an image sensor that is fixed in position relative to the camera body. The camera focuses on objects by moving a thin converging lens of focal length 50mm toward or away from the sensor along the principal axis.
(1) When the camera is focused on a bird perched 5.0m away, the distance between the lens and the sensor is measured to be 51.3mm. Calculate the required lens–sensor separation for a very distant landscape (object at effectively infinity).
(2) Determine the total range of travel the lens mount must provide to allow the camera to refocus from the distant landscape position found in part (a) to a nearby flower located 0.45m from the lens.
(3) Explain qualitatively why lenses in cameras with larger focal lengths require a greater range of travel for close-up focusing than lenses with shorter focal lengths.