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Optical systems:Magnifier, microscope, telescope & binoculars
Hecht 5.7
Wednesday October 9, 2002
2
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 ∞?∞?
3
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
4
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
25
FFoo FFoo
FFee
FFee
LL
hh
h’h’
h”h”
125
e
e f
cmM
5
Compound microscope
eoeo f
cm
f
LMMM
25
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
25
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
10
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
22
121
22
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