Geometrical Optics
Chapter 24
1
This week
This week we begin the study of optics. I have no idea
how far we will get into these chapters.
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Lenses & Mirrors
Interference
Diffraction
Probably not enough material to justify a 7:00AM class.
We can use office hours for that purpose.
There will be a quiz on Friday.
Watch for a new Mastering Physics (I know you just
can’t wait!)
Last quiz is in the bin.
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2
From the website:
Remaining Clicker Evil
Fix this evil or you will have a ZERO clicker score!!
Practice Problem Set (Monday Session)
****** TAKE NOTE OF THE FOLLOWING ******
The end of the semester is approaching. The common
Final Examination will be on Saturday, Dec 12, 2009 from 9AM-12PM
in room PSY 108
There will be one more exam this semester but it
probably will be on December 2 (Wednesday).
This exam will cover the remaining material covered. It will
also be covered in the final exam.
Don't forget to check the evil clicker file!
3
Geometrical Optics
Yup … more angle stuff!
4
Geometrical Process
Object
Image
Lens or
Mirror
Oh where, oh where, has my bug’s image gone .. oh where or where can it be???
5
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 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?






6
Same as the object,
Inverted (upside down)
Reverse
What kind of optics:
Mirror




Planar
Concave
Convex
Lens



converging
diverging
Where is the light?


7
Have you seen the light yet?
Note
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.
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Yes .. it can be confusing. We will attack this a point at
a time.
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8
Signs
9
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!!
10
11
12
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
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0.15
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0.20
0.20
0.20
0.15
0.21
0.21
0.21
0.22
0.22
0.22
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0.24
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0.24
0.25
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0.27
0.27
0.27
0.28
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0.29
0.29
0.29
0.30
0.30
0.30
0.31
13
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'
14
15
Curved Mirrors
For Student Misery Only!
16
Concave Mirror
con-CAVE
17
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.
18
Concave Mirror/Paraxial Approximation
   
   
   
     
    2

h
s

h
s'
h h
  2
s s'
MIRROR
EQUATION
19
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
20
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
21
What about here? R, s, s’
22
(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
23
Going Backwards
1 1 2
 
s s' R
R
2
s
(1/s  )
2
R
1
0
s'
s'  
24
More Better – A Parabola
surveillance
25
Image Formation
‘
‘
s0
R0
s'  0
y’<0
(from the diagram) so image is inverted.
26
The geometry……
 y'
(- sign frominvertedimage in diagram)
y
Similar T riangles,so
y  y'

and
s
s'
s'
ms
m
27
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
28
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
29
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
30
10 cm
eye
5 cm