1 optical systems: the eye, magnifier, microscope, telescope & binoculars hecht 5.7 monday...
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Optical systems:The eye, magnifier, microscope, telescope & binoculars Hecht 5.7
Monday October 7, 2002
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Human Eye, Relaxed
3.6 mm
7.2 mm
20 mm
n’ = 1.33
15 mm
F F’H H’
P = 66.7 D
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Accommodation Refers to changes undergone by lens to
enable imaging of closer objects Power of lens must increase There is a limit to such accommodation
however and objects inside one’s “near point” cannot be imaged clearly
Near point of normal eye = 25 cm Fully accommodated eye P = 70.7 for s =
25 cm, s’ = 2 cm
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Myopia: Near Sightedness
Eyeball too large ( or power of lens too large)
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Myopia – Near SightednessFar point of the eye is much less than Far point of the eye is much less than ∞, e.g. ∞, e.g. llff Must move object closer to eye to obtain a clear imageMust move object closer to eye to obtain a clear image
MyopicMyopic
F.P.F.P.
Normal N.P.Normal N.P.
MyopicMyopic
N.P.N.P.
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Myopiae.g. le.g. lff = 2m = 2m
fs
n
l f
1
'
'1
0.5 + 66.7 = 67.2 D0.5 + 66.7 = 67.2 D
is relaxed power of eye – too large!is relaxed power of eye – too large!
To move far point to To move far point to ∞, must decrease power ∞, must decrease power to 66.7to 66.7
Use negative lens with P = -0.5 DUse negative lens with P = -0.5 D
How will the How will the near point be near point be affected?affected?
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Laser Eye surgeryRadial Keratotomy – Introduce radial cuts to the Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeballcornea of the elongated, myopic eyeball
Usually use the 10.6 Usually use the 10.6 µm line of a COµm line of a CO22 laser for laser for
almost 100% absorption by the corneal tissuealmost 100% absorption by the corneal tissue
Front viewFront view
BlurredBlurredvisionvision
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Laser Eye surgeryRadial Keratotomy – Introduce radial cuts to the Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeballcornea of the elongated, myopic eyeball
Usually use the 10.6 Usually use the 10.6 µm line of a COµm line of a CO22 laser for laser for
almost 100% absorption by the corneal tissuealmost 100% absorption by the corneal tissue
Front viewFront viewFlatteningFlattening
Distinct Distinct visionvision
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Hyperopia – Far Sightedness
Eyeball too small – or lens of eye can’t fully accommodateEyeball too small – or lens of eye can’t fully accommodate
Image of close objects formed behind retinaImage of close objects formed behind retina
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Hyperopia – Far Sightedness
Suppose near point = 1mSuppose near point = 1m
Ds
n7.677.661
'
'
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Recall that for a near point of 25 cm, we need 70.7DRecall that for a near point of 25 cm, we need 70.7D
Use a positive lens with 3 D power to correct this Use a positive lens with 3 D power to correct this person’s vision (e.g. to enable them to read)person’s vision (e.g. to enable them to read)
Usually means they can no longer see distant Usually means they can no longer see distant objects - objects - Need bifocalsNeed bifocals
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Correction lenses for myopia and hyperopia
http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/V/Vision.html
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Hand magnifier
Observation with unaided eyeObservation with unaided eye
θθ
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MagnifierTo maximize the image, bring object as close to the eye To maximize the image, bring object as close to the eye as possible, i.e. bring object to near point s = las possible, i.e. bring object to near point s = ln n = 25 cm= 25 cm
θθmaxmax
mm
h
l
h
n 25max
h’h’
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Hand Magnifier
With thin lensWith thin lens
θθ’’
ff
FF
H,H’H,H’
hhMM’’
LL
s’s’
h”h”
ll
ssoo
What is the angular magnification of the What is the angular magnification of the image for an object at the near point or at image for an object at the near point or at ∞?∞?
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Compound Microscope
FFoo FFoo
FFee
FFee
LL
Wish to have intermediate image (h’) Wish to have intermediate image (h’) just inside the focus of the eyepiecejust inside the focus of the eyepiece
s’ s’ ≈ ≈ ffoo + L + L
xx
s = x + s = x + ffoo o
oo fx
fL
s
s
h
hM
''
Recall xx’ = Recall xx’ = ffoo22
x’x’
x’ x’ ≈ L≈ L
x = x = ffoo22/L/L
oo f
LM
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Recall: The magnification of an image formed Recall: The magnification of an image formed
(a)(a) at the near point isat the near point is
(b)(b)at infinity at infinity
Compound Microscope
ee f
cmM
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FFoo FFoo
FFee
FFee
LL
hh
h’h’
h”h”
125
e
e f
cmM
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Compound microscope
eoeo f
cm
f
LMMM
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Total magnificationTotal magnification
(Image at infinity)(Image at infinity)
1
25
eoeo f
cm
f
LMMM (Image at near point)(Image at near point)
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Compound Microscope
oo f
LM
ObjectiveObjective EyepieceEyepiece
10 X, 20 X, 40 X etc10 X, 20 X, 40 X etc
10X 10X
In most microscopes, L ~ 16 - 17 cmIn most microscopes, L ~ 16 - 17 cm
cmff
Lo
o
7.110
40X 40X ffoo = 0.4 cm = 0.4 cm
ee f
cmM
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ffee = 2.5 cm = 2.5 cm
Overall magnification M = 40X10 = 400Overall magnification M = 40X10 = 400
MMee = 10 = 10
(image at (image at ∞)∞)
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Compound Microscope
FFoo FFoo
FFee
FFee
LLA.S.
EnP
ExP
Where should the eye be located to view the image?Where should the eye be located to view the image?
Optimum viewing – Optimum viewing – Place eye near EPlace eye near ExxP (moving eye away decreases illumination and F.O.V.)P (moving eye away decreases illumination and F.O.V.)Ensure that exit pupil ~ same size as eye pupil!Ensure that exit pupil ~ same size as eye pupil!
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Compound Microscope
FFoo FFoo
FFee
FFee
LLA.S.
EnP
ExP
Chief RayChief Ray Marginal rayMarginal ray
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Numerical ApertureMeasure of light gathering powerMeasure of light gathering power
Cover GlassCover Glass
ααgg
ααaa
AirAirOilOil
ααgg’’ααoo
nngg
N. A. = n sin N. A. = n sin αα
LensLens
OO
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Numerical Aperture
aggnAN sin1sin..
If cover glass in airIf cover glass in air
ooogg nnAN sin5.1sin'sin..
If cover glass immersed in oil (no = 1.516) – between glassIf cover glass immersed in oil (no = 1.516) – between glassand oil there is essentially no refraction since nand oil there is essentially no refraction since ngg = 1.5 = 1.5
Increases the light gathering power by about 1.5Increases the light gathering power by about 1.5
(N.A. roughly analogous to f# of a lens)(N.A. roughly analogous to f# of a lens)
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Numerical Aperture
Core nCore n11
Cladding nCladding n22
Cladding nCladding n22
In optical fibresIn optical fibres
nnooααmaxmax
θθθθcc
N.A. = nN.A. = noosinsinααmaxmax= n= n11sin sin θθ = n = n11sin (90sin (90o o - - θθcc) = n) = n11cos cos θθcc2
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1 1 nnn
nn
This is a measure of the maximum cone of light acceptedThis is a measure of the maximum cone of light accepted
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Viewing distant objects, e.g. stars
ffeyeeyeθθ
Image size on retina h = Image size on retina h = ffeyeeyeθθ
starstar
hh
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Telescope
hhTT=f=feyeeyeθθ’’
ffoo ffee
ObjectiveObjective EyepieceEyepiece
s’s’
h”h”
h’h’
θθ’’
θθ’’θθ
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Telescope
ShowShow
e
o
f
fM (magnification of the telescope)(magnification of the telescope)
M
DD oexit (diameter of the exit pupil)(diameter of the exit pupil)
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The Hubble Space TelescopeThe Hubble Space Telescope
2.4 m primary2.4 m primarymirrormirror
0.3 m secondary0.3 m secondarymirrormirror
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BinocularsTwo telescopes side-by-sideTwo telescopes side-by-side
Prisms used to erect imagesPrisms used to erect images
EyepieceEyepiece
ObjectiveObjective
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Binoculars
““6 X 30”6 X 30”
Angular Magnification (M)Angular Magnification (M) Diameter of objective lens, DDiameter of objective lens, Doo (mm) (mm)
M
DD oexit
Exit pupil = 5 mm, a good match to the normal pupil diameterExit pupil = 5 mm, a good match to the normal pupil diameter
For night viewing, a rating of 7 X 50 is better: i.e. ~ 7 mmFor night viewing, a rating of 7 X 50 is better: i.e. ~ 7 mm