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25 Optical Instruments

• human eye

• microscopes & telescopes

• diffraction & resolution

• Homework:

• 6, 11, 13

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human eye• cornea & lens focus light to retina

• flexible lens alters focal length for near & far focus

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far-sightedness (hyperopia)

• cannot focus on near object

• correction requires converging lens

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near-sightedness (myopia)

• cannot focus on distant objects

• correction requires diverging lens

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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

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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

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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

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summary

• eye/instrument parameters

• eye defects & corrective lenses

• magnifying glass

• compound microscope

• refracting telescope

• diffraction limit of resolution

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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

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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 = /w

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compound microscope

• maximum AM ~ 2000x

• two converging lenses, one close to object (objective), other close to eye (eyepiece), fo < fe

• lens/lens distance = “L”

eo ff

LcmAM

)25(

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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

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refracting telescope

• practical maximum AM ~ (2)(apperture(mm))

• two converging lenses, fo > fe

• lens/lens distance ~ fo + fe

e

o

f

fAM