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Physics 1700
Geometric Optics
(rough draft)
W. Pezzaglia
Updated: 2012Aug21
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Geometric Optics
A. Focal Length
B. Lens Law, object & image
C. Optical Instruments
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A. Focal Length
1. Converging Lens (or Mirror)
2. Diverging Lens (or Mirror)
3. Lens Maker Equation
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1. Converging Systems
• Converging:
o Concave mirror
o Convex lens
• Light parallel to
principle axis
converges at the
“focal point”.
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2. Diverging Systems
• Diverging:
o Convex mirror
o Concave lens
• Focal length is “negative”
3. Lens Maker Equation
• Focal length “f” of a mirror with
radius of curvature “R”:
• Focal length “f” of a lens of
index “n” with radius of
curvature “R” (in air)
• For Lens “f” of index n2
submerged in medium of index
n 1:
R
f 
2
R
f 
n 1
R
f 
n2  n1
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3. Lens Maker Equation
• The more curved a lens or mirror, the
shorter the focal length.
• A bigger index of refraction makes a
shorter focal length lens.
• A lens underwater will have a longer focal
length than above water. Hence you
become “farsighted” underwater.
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B. Lens Law
1. Lens Equation
2. Virtual images
3. Lens combination
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1. Lens Equation (Gauss)
•
•
•
1 1 1
Distance to object “p”
 
f
p q
Distance to image “q”
If p>f then image will be “real” and
inverted.
2. Virtual Image
•
For converging lens if p<f then image will
be “virtual” and erect. [Magnifying glass]
•
[Diverging systems
only can make
virtual images.]
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3. Lens Combination
•
Two lenses (close
together) act as one lens
with focal length given by:
•
Example: eyeglasses.
Farsighted eye’s lens focal
length is too long. Adding
an extra lens shortens it.
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1
1
 
f
f1 f 2
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C. Optical Instruments
1. The Eye
2. Telescopes
3. Microscopes
1a Structure of eye
• Fovea of eye has best resolution (this is
what you are using to read), which only has
cones (color vision)
• Optic nerve creates a blind spot
• Lens is flexible
• Peripheral part of retina is mostly “rods”
which are black & white but can see much
fainter light (more than 10x)
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1b Color Perception
• Eye has 3 types of color
receptors (blue green red).
• Hence using just these
three colors can “trick” eye
into seeing nearly all colors
(can’t do violet)
• Your computer screen has
only these 3 colors!
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1c Eye: Farsighted
•
Hyperopia, also
known as
farsightedness
•
Cannot see clearly
closer than “near
point”
•
Correct with a
converging lens
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1c Eye: Nearsighted
•
Myopia or
nearsighted
•
Cannot see clearly
past “far point”
•
Correct with
diverging lens (focal
length equal to
negative of far
point)
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1c Astigmatism
•
Focal length
horizontal is not
same as vertical
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1c Astigmatism
Generically, means you can focus on one axis, but the other is out
of focus.
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1c Astigmatism
1d Binocular Vision
•Two eyes see slightly different images (due to
parallax).
•Brain puts it together to “see” 3D.
•Can “trick” brain into seeing 3D by giving each eye a
different picture (stereographs). Modern 3D movies
do it using polarization glasses.
Columbian Exposition 1893, stereograph,
viewer
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1d. 3D Vision
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1d. 3D Vision
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1e. Magnitudes and Brightness
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1.Magnitude Scale:
Hipparchus of Rhodes (160-127
B.C) assigns “magnitudes” to
stars to represent brightness.
The eye can see down to 6th
magnitude
1e Herschel Extends the Table
William Herschel (1738-1822) extended
the scale in both directions
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1e Herschel-Pogson Relation
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Herschel’s measurements suggested a 1st magnitude star is 100x more luminous
that a 6th magnitude one. Norman Pogson (1854) showed that this is because the
eye’s response to light is logarithmic rather than linear.
m  -2.5Logr 
22.5
C.3b
Gemini
Mag
MaMag
4 6
g
2
3
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2. Telescopes
• Our new telescope!
• Meade 14" LX200-ACF (f/10)
Advanced Coma-Free w/UHTC #1410-60-03
•
•
•
•
•
USD$ 6,999.00
Schmidt-Cassegrain Focus
Aperture 14 inch (356 mm)
Focal Length 3556 mm (f/10)
Resolution 0.321”
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2a Light Gathering Power
• Light Gathering Power (aka Light Amplification)
is proportional to area of mirror
• More light, can see fainter (more
distant) objects.
• Aperture=diameter of objective mirror (for our
telescope its 14 inches=356 mm)
 Aperture objective
LGP  
Aperture eye




2
2
 356 mm 
  3520 
 
 6 mm 
more than eye
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2b Limiting Magnitude
• Consulting table, a LGP of 3520 translates to
more than 8.5 magnitudes. Exact calculation:
m  2.5 Log (3520)  8.87
• Limiting magnitude of naked eye is +6, can see
over 8000 stars.
• hence looking through scope we can see up to
+14.8 or over 100,000,000 stars in our galaxy,
and over 1000 galaxies!
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2c. Basic Telescope Design
Refractor Telescope (objective is a lens)
Focal Length of Objective is big
Focal Length of eyepiece is small
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2d Chromatic Aberration
Different colors are bent (refracted) at slightly different angles, with
red light focusing the furthest away. Difficult to get a sharp color
picture. Problem with refracting telescopes
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2e Newtonian Reflecting Telescope
• Objective is a mirror, no chromatic problems!
• Focal length is approximately the length of tube
• Light is directed out the side for the eyepiece
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2f Schmidt Cassegrain Reflecting Telescope
• Cassegrain focus uses “folded optics” so the
focal length is more than twice the length of tube
• Light path goes through hole in primary mirror
• Schmidt design has corrector plate in front
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2. Magnification Power
The overall magnification of the angular size is
given by the ratio of the focal lengths
Power  
Fobjective
Feyepiece
For our scope (F=3556 mm), with a 26 mm
eyepiece, the power would be:
3556 mm
Power  
 137 
26 mm
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2g. Too Much Magnification?
• Extended objects (planets, nebulae, galaxies) when
magnified more will appear fainter
Low Power
High Power
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2h. Too Much Magnification?
• Too much magnification and you won’t see it at all!
• Its about surface brightness! Your eye can’t see below a
certain amount.
Low Power
High Power
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3. Microscopes (briefly)
• Creates a BIG virtual image 25 cm away from the
eye.
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D. References
• Lick Observatory Video:
http://www.youtube.com/watch?v=g63lk_0kngk
• Video: Mechanical Universe #40, Optics
• Stereographs: http://www.library.hbs.edu/hc/pc/stereograph.html
• Stereograph: http://www.sun.travel.pl/stereoscope&page=6