Optical systems: The eye, magnifier, microscope, telescope

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Optical systemsThe eye, magnifier, microscope,
telescope binoculars

• Hecht 5.7
• Monday October 7, 2002

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(No Transcript)
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Human Eye, Relaxed
20 mm
15 mm
n 1.33
F
H
H
F
3.6 mm
P 66.7 D
7.2 mm
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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 ones 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 Sightedness
Far point of the eye is much less than 8, e.g. lf
Must move object closer to eye to obtain a clear
image
Normal N.P.
Myopic F.P.
Myopic N.P.
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Myopia
e.g. lf 2m
How will the near point be affected?
0.5 66.7 67.2 D
is relaxed power of eye too large!
To move far point to 8, must decrease power to
66.7
Use negative lens with P -0.5 D
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Laser Eye surgery
Radial Keratotomy Introduce radial cuts to the
cornea of the elongated, myopic eyeball
Usually use the 10.6 µm line of a CO2 laser for
almost 100 absorption by the corneal tissue
Blurred vision
Front view
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Laser Eye surgery
Radial Keratotomy Introduce radial cuts to the
cornea of the elongated, myopic eyeball
Usually use the 10.6 µm line of a CO2 laser for
almost 100 absorption by the corneal tissue
Distinct vision
Front view
Flattening
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Hyperopia Far Sightedness
Eyeball too small or lens of eye cant fully
accommodate
Image of close objects formed behind retina
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Hyperopia Far Sightedness
Suppose near point 1m
Recall that for a near point of 25 cm, we need
70.7D
Use a positive lens with 3 D power to correct
this persons vision (e.g. to enable them to read)
Usually means they can no longer see distant
objects - Need bifocals
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Correction lenses for myopia and hyperopia
http//users.rcn.com/jkimball.ma.ultranet/BiologyP
ages/V/Vision.html
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Hand magnifier
Observation with unaided eye
?
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Magnifier
To maximize the image, bring object as close to
the eye as possible, i.e. bring object to near
point s ln 25 cm
h
?max
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Hand Magnifier
What is the angular magnification of the image
for an object at the near point or at 8?
With thin lens
H,H
h
?
F
hM
so
l
f
s
L
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Compound Microscope
x
L
Fe
Fo
Fo
Fe
Recall xx fo2
x
x L
Wish to have intermediate image (h) just inside
the focus of the eyepiece
x fo2/L
s fo L
s x fo
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Compound Microscope
L
Fe
h
h
Fo
Fo
Fe
h

• Recall The magnification of an image formed
• at the near point is
• at infinity

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Compound microscope
Total magnification
(Image at infinity)
(Image at near point)
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Compound Microscope
In most microscopes, L 16 - 17 cm
Objective
Eyepiece
(image at 8)
10 X, 20 X, 40 X etc
fe 2.5 cm
10X ?
Me 10
40X ? fo 0.4 cm
Overall magnification M 40X10 400
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Compound Microscope
L
A.S.
Fe
Fo
Fo
Fe
EnP
ExP
Where should the eye be located to view the image?

• Optimum viewing
• Place eye near ExP (moving eye away decreases
  illumination and F.O.V.)
• Ensure that exit pupil same size as eye pupil!

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Compound Microscope
L
A.S.
Fe
Fo
Fo
Fe
EnP
ExP
Chief Ray
Marginal ray
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Numerical Aperture
Measure of light gathering power
N. A. n sin a
Lens
Air
Oil
ag
ag
ao
aa
Cover Glass
ng
O
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Numerical Aperture
If cover glass in air
If cover glass immersed in oil (no 1.516)
between glass and oil there is essentially no
refraction since ng 1.5
Increases the light gathering power by about 1.5
(N.A. roughly analogous to f of a lens)
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Numerical Aperture
In optical fibres
Cladding n2
Core n1
?c
?
no
amax
Cladding n2
N.A. nosinamax n1sin ? n1sin (90o - ?c)
n1cos ?c
This is a measure of the maximum cone of light
accepted
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Viewing distant objects, e.g. stars
star
h
?
feye
Image size on retina h feye?
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Telescope
Objective
Eyepiece
fo
fe
hTfeye?
?
?
h
?
h
s
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Telescope
Show
(magnification of the telescope)
(diameter of the exit pupil)
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The Hubble Space Telescope
0.3 m secondary mirror
2.4 m primary mirror
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Binoculars
Two telescopes side-by-side
Prisms used to erect images
Objective
Eyepiece
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Binoculars
6 X 30
Angular Magnification (M)
Diameter of objective lens, Do (mm)
Exit 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 mm