At a pair of conjugate planes ( ) between input medium and output medium

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Optics & Photonics · Geometrical optics and imaging

What an Instrument Can See, Ch The paraxial system as an operator

Problem

At a pair of conjugate planes (B=0B=0) between input medium n1n_1 and output medium n2n_2, the transverse magnification is MT=AM_T=A. Define the real-angle angular magnification MA=θ2/θ1M_A=\theta_2/\theta_1, the ratio of the real ray angles at the two planes, for the ray leaving the axial object point. ((a)) Show that MA=Dn1/n2M_A = Dn_1/n_2, and hence that MTMA=n1/n2M_TM_A = n_1/n_2, generalising the familiar MTMA=1M_TM_A=1 that holds when the two media match. ((b)) A single spherical surface of radius R=25 mmR=25\ \mathrm{mm} separates air (n1=1.00n_1=1.00) from glass (n2=1.50n_2=1.50); a point object stands so=100 mms_o=100\ \mathrm{mm} in front of it, in air. Find sis_i, MTM_T and MAM_A, and verify the relation of part (a) numerically.

Browse the problem library