A shopkeeper fits a hemispherical safety mirror at the entrance of his store. The mirror has a radius of curvature of 1.5m. A man 1.8m tall stands 2.0m in front of the mirror on its principal axis.
(a) Find the focal length of the mirror.
(b) Calculate the position of the image of the top of the man's head relative to the mirror.
(c) Determine the height of the image formed and comment on its nature and orientation.
(d) If the same mirror were concave with the same magnitude of focal length and the man stood at the same distance, calculate the new image position and height. Explain briefly how the nature and orientation of the image would change.