Physic Labs

Problem 3

An object is placed at distance do>fd_o>f from a converging thin lens of focal length ff. Find image distance did_i and signed magnification mm; real images have di>0d_i>0. The thin lens is in air, and an object of height hoh_o is perpendicular to the principal axis; a real image forms on the opposite side. (a) Find did_i from the lens equation. (b) Find the signed magnification mm. (c) Find signed image height hih_i and state whether the image is upright or inverted. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
di=fdodo−f,m=−fdo−f,hi=−fhodo−f\boxed{d_i=\frac{fd_o}{d_o-f},\quad m=-\frac{f}{d_o-f},\quad h_i=-\frac{f h_o}{d_o-f}}
problems.proof.analysis

The final expressions are collected in the order requested and must satisfy the equations used above. Checking dimensions, signs, and limiting conditions catches algebra errors or omitted constraints.