Physic Labs

Problem 3

A small real object of height hoh_o is placed in front of a thin converging lens of focal length f>0f>0, at distance do>fd_o>f from its optical center, with the principal axis perpendicular to the lens. Use the convention that a real object has do>0d_o>0, a real image on the far side has di>0d_i>0, and lateral magnification is m=−di/dom=-d_i/d_o, with lens equation 1/f=1/do+1/di1/f=1/d_o+1/d_i. (a) Derive the image position. (b) Find mm and image height hih_i. (c) Classify the image and examine the limit do→f+.d_o\to f^+.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
hi=mho=−fdo−fhoh_i=mh_o=-\frac{f}{d_o-f}h_o
problems.proof.analysis

Lateral magnification is the ratio m=hi/hom=h_i/h_o. Since m<0m<0, the signed image height is negative on the chosen axis, representing an inverted image.