Physic Labs

Problem 3

A transverse object of height HH is placed before a converging thin lens of focal length f>0f>0, perpendicular to its principal axis. Its distance from the lens is u=3fu=3f; use the convention that image distance v>0v>0 lies opposite the object and signed transverse magnification is M=−v/uM=-v/u. (a) Use the principal-ray construction to determine the image character and location. (b) Find the signed magnification and image height. (c) If a smaller object is placed at the same position, state what changes and what does not, explaining with the lens equation.
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v=3f2,M=−12,H′=−H2(image reˊelle, renverseˊe)\boxed{v=\frac{3f}{2},\quad M=-\frac12,\quad H'=-\frac H2}\quad\text{(image réelle, renversée)}
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The image is real, inverted, on the far side, and half as tall as the object. Changing object height without changing its distance leaves image position and magnification unchanged.

problems.proof.pitfall. Keep the sign convention consistent and retain only physically meaningful roots or directions.