A laboratory benchtop setup uses a single thin glass lens of focal length 15 cm mounted a fixed distance of 50 cm from a movable projection screen, as shown in the verbal description below.
• The lens is held rigidly in a vertical holder.
• A translucent screen can slide along a rail that is rigidly fixed 50 cm from the lens.
• An illuminated arrow will be placed somewhere along the axis on the opposite side of the lens so that a sharp image appears on the screen.
Answer the following questions about the placement of the arrow and the resulting image.
(a) Derive an algebraic equation that relates the arrow’s distance from the lens to the requirement that a sharp image forms on the screen 50 cm away. Show all reasoning without substituting numbers at this stage.
(b) Solve the equation you obtained in part (a) to determine all allowable numerical positions of the arrow (measured from the lens) that satisfy the focusing requirement.
(c) For each allowable arrow position found in part (b), calculate the corresponding numerical lateral magnification and state whether the image is upright or inverted.
(d) Explain, without additional calculation, why no other arrow positions could produce a sharp image on the screen in this setup.
(e) One of the allowable arrow positions produces an image larger than the object. Identify which one and provide a physical explanation, referencing properties of rays passing through the lens.