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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1v=1f−13f=23f,v=3f2>0\frac1v=\frac1f-\frac1{3f}=\frac2{3f},\quad v=\frac{3f}{2}>0
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Putting u=3fu=3f into the equation gives an image 3f/23f/2 from the lens. The positive sign means a real image on the far side.