International Physics Olympiad · Year 2004

Problems

Problem 1An object is placed at distance $d_o>f$ from a converging thin lens of focal length $f$ . Find image distance $d_i$ and signed magnification $m$ ; real images have $d_i>0$ . The thin lens is in air, and an object of height $h_o$ is perpendicular to the principal axis; a real image forms on the opposite side. (a) Find $d_i$ from the lens equation. (b) Find the signed magnification $m$ . (c) Find signed image height $h_i$ 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.Solutions: 1
Problem 2A particle of mass $m$ and charge $q$ moves perpendicular to a uniform magnetic field $B$ at speed $v$ . Find orbit radius and period; use $|q|$ for charge magnitude. The magnetic field is perpendicular to the initial velocity; neglect gravity and collisions. (a) Use the Lorentz force to find orbit radius $r$ . (b) Find the orbital period $T$ . (c) Find the cyclotron frequency and identify which result is independent of speed $v$ . 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.Solutions: 1
Problem 3Light of frequency $f$ illuminates a metal with work function $\phi$ . Find the maximum photoelectron kinetic energy and stopping potential; use Planck constant $h$ and electron charge magnitude $e$ . Each photon carries energy $hf$ ; electrons are emitted only when the light exceeds the threshold frequency. (a) Find threshold frequency $f_0$ . (b) For $f>f_0$ , find maximum kinetic energy $K_{max}$ . (c) Find stopping potential $V_s$ and state the emission condition. 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.Solutions: 1