Physic Labs

Problem 3

A thin converging lens has focal length f>0f>0. A real object of height hh is placed a distance u>fu>f from the lens. Find the signed image distance vv, magnification mm, image height, and whether the image is real or virtual. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
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m=−vu=−fu−fm=-\frac vu=-\frac{f}{u-f}
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Ray geometry and similar triangles give signed transverse magnification m=−v/um=-v/u; the negative sign means inversion. This follows from the chosen physical model and the stated initial conditions; the sign convention must remain consistent throughout. A dimensional check catches algebraic errors before the result is interpreted.