A convex mirror is mounted in a loading dock in order to provide a wide field of view. This convex mirror is spherical, with a 90 cm radius of curvature. A simple camera is placed in front of this mirror to monitor the activity in the loading dock. The camera consists of a single converging lens of focal length 3.75 cm, placed 4.0 cm in front of a CCD array. A truck enters the loading dock and stops at a position 25 m in front of the mirror.
(a) Consider the image of the truck formed by the convex mirror. Where is this image located relative to the mirror?
(b) Could a person standing in front of the convex mirror see an image of the truck? If so, what sort of image would it be? (Upright or inverted? Magnified or diminished?)
(c) Where should the camera be placed to provide a focused image of the truck? Give the distance x between the convex mirror and the camera lens.
(d) If one half of the camera lens were covered up, what would happen to the image recorded by the camera? Would half of it disappear?
