Geometrical Optics
Chapter 24
1
This week
This week we will cover some topics in geometrical optics.
This will include mirrors and lenses. This is about all that we
will be able to accomplish.
There will be NO QUIZ this week.
Examination #4 will be on Monday, Dec. 6th. (One Index Card)
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AC circuits
Optics per whatever we manage to cover.
The final exam will be on Saturday, December 11th at 7:00 AM
in room HPA 119. (Two Index Cards allowed)
 Entire semesters work.
 Joint exam with other Studio Class.
Watch for new WebAssign and probably one after that.
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2
Please Note:
An earlier notification incorrectly listed the period for
student submission of the course evaluation, the
Student Perception of Instruction. The final date for
completion of the Student Perception of Instruction
is the last day of classes, December 6 at 11:59 pm.
We apologize for any confusion.
3
About the final examination and exam #4
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4
Only topics discussed in class, contained in
the lab sheets, included in WebAssigns or
assigned for reading will be covered on these
exams.
Bring ALL Lab Units from Magnetism Through
Optics to class on Friday. One of them will be
collected for grading.
STUDIO UNIT ???
5
Geometrical Optics
Yup … more angle stuff!
6
Geometrical Process
Object
Image
Lens or
Mirror
Oh where, oh where, has my bug’s image gone .. oh where or where can it be???
7
Where’s the image, where’s the object … who
cares??? We do!
Questions about the image:
What kind of an image is it?
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Real
Virtual
Where is the object, where is the image?
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Behind the lens
In front of the lens
Where is the light coming from? Where is it going?
What is the size of the image? (magnification)
What is the orientation of the image?
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Same as the object,
Inverted (upside down)
Reverse
What kind of optics:
Mirror
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Planar
Concave
Convex
Lens
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converging
diverging
Where is the light?
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Have you seen the light yet?
mirrors
Note
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The object is usually the source of light.
The image is where the light converges to replicate the
object.
The image can be on either side of the “optical
element”
The image can be real or virtual
The image can form an object for a second optical
element.
Yes .. it can be confusing. We will attack this a point at
a time.
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Signs – We mean (-) or (+)

The distance from the object to the lens/mirror is called
the object distance.
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The distance from the image to the lens/mirror is called
the image distance.
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It is positive if it is on the same side of the optical element
as the incoming light. Otherwise it is negative
It is designated by s
It is positive if it is on the same side as the outgoing light
It is designated by s’. Otherwise it is negative.
Without this sign convention, these problems would be
much more difficult. So pay attention to them!!
11
Consider looking in a plane mirror in your
bathroom. Your image distance is
A.
B.
C.
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Positive
Negative
This convention doesn’t apply to my bathroom mirror.
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14
Paraxial Rays : Small Angle Approximation
theta
sin
tan
0.01
0.01
0.01
0.02
0.02
0.02
0.03
0.03
0.03
0.04
0.04
0.04
0.05
0.05
0.05
0.06
0.06
0.06
0.07
0.07
0.07
0.08
0.08
0.08
0.09
0.09
0.09
0.10
0.10
0.10
0.11
0.11
0.11
0.12
0.12
0.12
0.13
0.13
0.13
0.14
0.14
0.14
0.15
0.15
0.15
0.16
0.17
0.16
0.17
0.16
0.17
0.18
0.18
0.18
0.19
0.19
0.19
0.20
0.20
0.20
0.20
0.15
0.21
0.21
0.21
0.22
0.22
0.22
0.23
0.23
0.23
0.24
0.24
0.24
0.25
0.25
0.26
0.26
0.26
0.27
0.27
0.27
0.28
0.28
0.28
0.29
0.29
0.29
0.30
0.30
0.30
0.31
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sin   
tan  sin   
0.45
0.40
0.35
0.30
0.25
0.10
0.05
0.00
0.00
0.10
0.20
0.30
0.40
y'
m
1
y
s   s'
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17
Curved Mirrors
For Student Misery Only!
18
Concave Mirror
con-CAVE
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Sign Convention
When the Center of Curvature
is on the same side of the
outgoing ray, R is positive.
Otherwise, if the center of
curvature is not on the same side
as the outgoing ray, R is negative.
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Concave Mirror/Paraxial Approximation
   
   
   
     
    2

h
s

h
s'
h h
  2
s s'
MIRROR
EQUATION
21
The normal to the
surface passes
through C
Therefore

h
R
Consequently
h h 2h
 
s s' R
1 1 2
 
s s' R
For this structure
A.
B.
C.
D.
The Radius R is positive and s’ is negative
The Radius R is negative and s’ is negative
R is positive and s’ is positive
R is negative and s’ is positive
Answer
22
When the Center of Curvature
is on the same side of the
outgoing ray, R is positive.
the image distance is positive if it is on
the same side as the outgoing light
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This image is
A. real, reversed
B. virtual, not reversed
C. real, not reversed
D. virtual, reversed
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What about here? R, s, s’
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(convex mirror)
Concept: Focal Length of a Mirror
1 1 2
 
s s' R
s   (1/s  0)
R
f  s' 
2
1 1 1
 
s s' f
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Going Backwards
1 1 2
 
s s' R
R
2
s
(1/s  )
2
R
1
0
s'
s'  
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For a convex mirror, the Radius
A.
B.
C.
D.
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Is positive
Is negative
The sign depends on the position of the image.
The sign depends on the current sign of the
zodiac.
When the Center of Curvature
is on the same side of the
outgoing ray, R is positive.
Otherwise, if the center of
curvature is not on the same side
as the outgoing ray, R is negative.
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Image Formation – Ray Diagram
‘
‘
s0
R0
s'  0
y’<0
(from the diagram) so image is inverted.
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Complete Unit 18
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