A student investigates three different spherical mirrors. For each mirror she records the signs (positive or negative) of the focal length f and of the image distance si when an object is placed in front of the mirror. The results are shown below.
Case I: f is positive, si is positive.
Case II: f is negative, si is negative.
Case III: f is positive, si is negative.
(a) For each case, identify the mirror as concave, convex, or plane and justify your choice based on the recorded signs.
(b) In Case I the object distance is 30cm and the image distance is 45cm. Calculate the focal length and comment on whether the computed value is consistent with the identification made in part (a).
(c) In Case II the object distance is 20cm and the magnitude of the image distance is 8cm. Determine the magnification and state whether the image is reduced or enlarged.