A student places a luminous arrow 40 cm in front of a thin lens of unknown type. The lens produces a sharp image that is inverted and half the height of the object on a screen located on the opposite side of the lens.
(a) Describe what the fact that the image is inverted and smaller than the object tells you about the relative positions of the object, the image, and the focal region of the lens.
(b) Based on this information, explain whether the lens must be converging or diverging. Justify your answer without performing numerical calculations.
(c) Using an appropriate sign convention for focal length, state whether the focal length of this lens is positive or negative and explain your reasoning.
(a) Describe what the observed image characteristics imply about object, image, and focal positions.
(b) Explain and justify whether the lens is converging or diverging.
(c) Indicate the sign of the focal length under a standard sign convention and justify.