Problem 3
A thin converging lens has focal length . A planar object perpendicular to the principal axis is placed a distance from the lens. Using the thin-lens model and the convention that real images have positive image distance, find the signed image distance , lateral magnification , and describe the image. Use the stated signed-distance convention and assume a sufficiently small object so the paraxial approximation applies. (a) Determine the image position from the conjugate equation. (b) Calculate the magnification and image height if the object height is . (c) Decide whether the image is real or virtual and upright or inverted, and check the dimensional consistency.
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The image lies on the opposite side of the lens, at distance . It is real, inverted, and half as tall as the object.