25 Optical Instruments human eye microscopes & telescopes diffraction & resolution Homework: 6, 11, 13

human eye cornea & lens focus light to retina flexible lens alters focal length for near & far focus

far-sightedness (hyperopia) cannot focus on near object correction requires converging lens

near-sightedness (myopia) cannot focus on distant objects correction requires diverging lens

near (NP) and far (FP) points eye focus: 25cm to very far, i.e. NP = 25cm, FP = infinity far-sighted: NP > 25cm, corrective lenses allow focus at 25cm, e.g. reading glasses near-sighted: FP < infinity, corrective lenses allow focus at infinity, e.g. needing glasses to drive a car

near-sighted correction when do = infinity, -di = FP (contacts) thus -f = FP, 1/f = -1/FP Ex. looking along ruler, a student cannot focus past 20cm FP = 20cm 1/f = -1/0.20m = -5.0D

far-sighted correction when do = 25cm, -di = NP (contacts) thus 1/f = 1/25 - 1/NP (1/do + 1/di) Ex. a parent reads newspaper at arm’s length, 1.0m NP = 1.0m 1/f = 1/0.25m - 1/1.0m = +3.0D

summary eye/instrument parameters eye defects & corrective lenses magnifying glass compound microscope refracting telescope diffraction limit of resolution

magnifying glass allows close-focus object at focal point - eye focuses parallel rays which emerge angular magnification (AM) = 25cm/f AM = angular-width ratio: with lens vs. when 25cm from eye

diffraction & resolution diffraction thru aperture limits the ability to separate (resolve) two objects limit of resolution defined = coincidence of 1st dark fringe with CM (below right). min. angle resolved for single slit = l/w

compound microscope maximum AM ~ 2000x two converging lenses, one close to object (objective), other close to eye (eyepiece), fo < fe lens/lens distance = “L”

optical instruments objective lens faces object aperture – diameter of light passing through objective lens (can be controlled, e.g. “f-stop”) small aperture gives large “depth of field”, i.e. near & far are in focus

refracting telescope practical maximum AM ~ (2)(apperture(mm)) two converging lenses, fo > fe lens/lens distance ~ fo + fe