A thin convex lens of focal length 15cm is used in an optical bench experiment.
a. (i) Derive an expression for the object distance u required to obtain a linear magnification m in terms of the focal length f and m.
b. (ii) Using your result, calculate the object distance when the desired magnification is +2.
c. (iii) Repeat the calculation for a magnification of −2.
d. (iv) For each case obtained in (ii) and (iii), determine the corresponding image distance and state clearly whether the image is real or virtual, erect or inverted.