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(III) A bright object is placed on one side of a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. The distance dT = di + dO between the object and the screen is kept fixed, but the lens can be moved. (a) Show that if dT > 4f, there will be two positions where the lens can be placed and a sharp image will be produced on the screen. (b) If dT < 4f, show that there will be no lens position where a sharp image is formed. (c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.
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