For a thin convex lens of focal length f, an object is placed on the principal axis and a real, inverted image of the same size as the object is obtained.
(a) Derive an expression relating the object distance u with the focal length f under the above condition.
(b) Using the result of part (a), find the numerical value of u for a lens of focal length 15cm.
(c) If the object is now moved 5cm closer to the lens from the position obtained in part (b), calculate the new image distance and magnification, and comment on the change in the nature and size of the image.