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
1f=1do+1di\frac1f=\frac1{d_o}+\frac1{d_i}
problems.proof.analysis

For a thin lens in air, the lens equation relates focal length to signed object and image distances. The stated convention assigns positive distances to the real object and far-side real image.

problems.proof.pitfall. Keep the sign convention consistent; do not mix in a formula using another convention.