A digital camera uses a thin converging lens of focal length 50 mm to project an image onto a sensor that is fixed 55 mm behind the lens. To accommodate objects at different distances, only the lens can be translated forward or backward; the sensor remains fixed.
For this question, distances are measured from the center of the lens along the optical axis.
(a) Derive an expression for the object distance in terms of the sensor distance (55 mm) and the focal length.
(b) Use your expression from part (a) to calculate the closest object distance that can be brought into sharp focus without moving the sensor.
(c) Calculate the magnification for the closest-focus condition obtained in part (b) and state whether the image on the sensor is upright or inverted.
(d) Suppose the photographer instead wishes to focus on a mountain peak far away (assume the object distance approaches infinity). Determine how far, if at all, the lens must be shifted relative to the sensor to achieve focus, and explain your reasoning.
(e) Discuss qualitatively how the range of object distances that can be focused would change if the camera employed a lens of shorter focal length while keeping the same 55 mm sensor distance.