1 25 optical instruments human eye microscopes & telescopes diffraction & resolution...
TRANSCRIPT
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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