Inside an instrument

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

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

Problem

Inside an instrument, air (n=1n=1) fills the space at two reference planes: the plane of an aperture, and the plane where the rest of the system forms an image of that aperture, so the two planes are conjugate. At the aperture the marginal ray has height y1=8 mmy_1 = 8\ \mathrm{mm}, and the chief ray, which crosses the axis there, has angle θˉ1=0.05 rad\bar\theta_1 = 0.05\ \mathrm{rad}. At the image of the aperture the marginal ray has height y2=4 mmy_2 = 4\ \mathrm{mm}. ((a)) Explain why the chief ray also crosses the axis at the second plane, and use the Lagrange invariant to find the chief-ray angle θˉ2\bar\theta_2 there. ((b)) Give the transverse magnification MT=y2/y1M_T = y_2/y_1 and the angular magnification MA=θˉ2/θˉ1M_A = \bar\theta_2/\bar\theta_1 between the two planes, and confirm MTMA=1M_TM_A = 1.

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