Geometrical Optics
14.2
1
Getting There Fast – Are you studying for the final yet??
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
1
2
3
4 Complete
Induction
5
6
AC
7
8
AC
Quiz?
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10
11
COMPLETE
AC EXPT
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13 OPTICS
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15 OPTICS
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17
18
EXAM #3
(No Optics)
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20 OPTICS
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22 OPTICS
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24
25 (LAST LASS)
OPTICS
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27
28
29
30 FINAL
HPA 119
9:00 AM
2
EM Waves
POLARIZATION
Quiz
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.
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
Only what we cover in class will be covered on the final examination.
There will be NO QUIZ this week.
The final exam will be on Saturday, April 30th 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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3
Next Week
Monday
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Post Test (will be used for borderline cases)
Complete topics and possibly some problems
Wednesday-Friday
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If there is coordinated interest, I might be able to come to
campus and go over some problems. Need to find some
common day/time to do this.
Saturday
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4
Final Examination (2 index cards allowed).
About the final examination

Only topics discussed
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will be covered on the final exam.
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5
In class,
On class PowerPoint lectures
Contained in the lab sheets,
Included in WebAssigns or
Assigned for reading
That’s a lot of stuff!
Bring ALL Lab Units from Magnetism Through
Optics to class on Friday. One of them will be
collected for grading.
STUDIO UNIT ???
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Geometrical Optics
Yup … more angle stuff!
7
Geometrical Process
Object
Image
Lens or
Mirror
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Where’s the image, where’s the object … who
cares??? We do!
Questions about the image:
What kind of an image is it?



Real
Virtual
Where is the object, where is the image?


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Behind the mirror
In front of the mirror
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




Lens



Planar
Concave
Convex
converging
diverging
Where is the light?

10
Have you seen the light yet?
mirrors
Note
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
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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. You have done some of this in the units so this
is a review of sorts.
11
Signs – We mean (-) or (+)

The distance from the object to the lens/mirror is called
the object distance.



The distance from the image to the lens/mirror is called
the image distance.



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!!
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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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15
Paraxial Rays : Small Angle Approximation
theta
sin
tan
0.01
0.01
0.01
0.02
0.02
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0.15
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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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18
Curved Mirrors
For Student Misery Only!
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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
   
     (external angle)
   
     
    2

h
s

h
s'
h h
  2
s s'
MIRROR
EQUATION
22
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
23
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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Continue the current Unit
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Examples to review
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A concave spherical mirror has a radius of 10 cm. Calculate
the location and size of an 8mm object a distance 15 cm
from the mirror.
1 1 2 1
  
s s' R f
s '  7.5
 s'
m
 .5
s
y  4 mm
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10 cm
5 cm
Normal to mirror
and bounces back
along incoming
path.
A concave spherical mirror has a radius of 10 cm. Calculate
the location and size of an 8mm object a distance 10 cm
from the mirror.
1 1 2 1
  
s s' R f
s '  10cm
 s'
m
 1.0
s
y  8 mm
35
10 cm
5 cm
A concave spherical mirror has a radius of 10 cm. Calculate
the location and size of an 8mm object a distance 2.5 cm
from the mirror.
virtual
image
1 1 2 1
  
s s' R f
s '  5cm
 s'
m
 2.0
s
y  8 mm
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10 cm
eye
5 cm
The Concave Mirror
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More Convex Mirror
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Graphical Methods are very useful to check
your work.
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