Lecture 38:Lecture 38: WED 22 APRWED 22 APRPhysics 2102Jonathan DowlingOptics: ImagesOptics: ImagesThe human eyeThe human eye consists of avariable-geometry lens (crystalline)which produces a real image on a“screen” (retina) which is transmittedto the brain via the optical nerve.The cristalline automatically adjusts itself so we see well any objectplaced between infinity and a distance called “near point” (about 25cmfor a typical 20 year old). The “image distance” is the eye diameter~2cm.Optical Instruments: the human eyeOptical Instruments: the human eyeOptical instruments: combinationOptical instruments: combinationof several (thin) lensesof several (thin) lensesF1F1F2F2If lenses are very close, the compound lens has 1/f~1/f1+1/f2Corrective GlassesCorrective GlassesA farsighted person needs a convergent lens.A nearsighted person needs a divergent lens.The “power” of a lens is measured in dioptres: P=1/f with f is in m.Glasses with -6D are divergent glasses with f=− 1/6D =−0.17m=−17cmThe dioptres add! Two lenses have 1/f=1/f1+1/f2 → D=D1+D2The magnification of an object is m=i/p~iθ/h,but i=eye diameter.Maximum magnification: m~2cm/25cm (!?)Angular magnification (different from lateral): mθ=θ’/θ. fcmfhcmh 25m ' 25=!="""Magnifying lensMagnifying lensWe’d like to make p smaller (move the object closer). We use amagnifying lens to produce a (larger) image than our eye can see:Very near the focus!Microscope:To increase the magnification of a lens, one wants to have a shortfocal length. That means small radii of curvature (very curved lens).This, in turn implies a lot of aberration (one is immediately out ofthe thin lens approximation). A solution to this is obtained bycombining two lenses. The resulting device is called microscope.pim !=Object O is magnifiedby the objective:And its image is magnifiedby the eyepiece:fcmm25=!Total magnification:eyobfcmfsmmM25!=="Telescope:Telescopes are arrangement of lenses that improve vision of objectsvery far away. They are configured like a microscope. However, theobjective forms an image essentially at its focus, and therefore theeyepiece’s focus has to be placed at that same point.The magnification is given bythe ratio θey/θob, and sinceobobfh /'=!eyeyfh /'=!eyobffm !=Refracting telescopes are of limiteduse (chromatic aberration). Reflectingtelescopes built with mirrors are preferred in astronomy.ExampleExampleThe world’s largest refracting telescope is at the YerkesObservatory of the University of Chicago at Williams Bay,Wisconsin. The objective has a diameter of 102cm and a focallength of 19.5m. The focal length of the eyepiece is 10cm. What isits magnifying power?1951.05.19!=!=!=mmffmeyobWhy so large (102cm)? Because thelarger the objective, the more light itgathers.Reflective telescopesReflective telescopesKeck observatory (MaunaKea, Hawaii) and theHale-Bopp comet.Largest optical telescope,composed of 36 (!)hexagonal mirrorsegments performing as asingle mirror 10m
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