GEO1 (2).ppt

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.
 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.
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
Lens or
Mirror
Object
Image
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!
 What kind of an image is it?
 Real
 Virtual
 Where is the object, where is the image?
 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?
 Same as the object,
 Inverted (upside down)
 Reverse
Questions about the image:
6

What kind of optics:
 Mirror
 Planar
 Concave
 Convex
 Lens
 converging
 diverging
 Where is the light?
 Have you seen the light yet?
7

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.
 Yes .. it can be confusing. We will attack this a
point at a time.
8

Signs – We mean (-) or (+)
 The distance from the object to the lens/mirror is
called the object 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
 The distance from the image to the lens/mirror is
called the image distance.
 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

Paraxial Rays : Small Angle Approximation








sin
tan
sin
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
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 0.16 0.16
0.17 0.17 0.17
0.18 0.18 0.18
0.19 0.19 0.19
0.20 0.20 0.20
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
13

'
1
'
s
s
y
y
m




14

Curved Mirrors
For Student Misery Only!
16

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














2
'
'




s
h
s
h
s
h
s
h
The normal to the
surface passes
through C
Therefore
R
h


Consequently
R
s
s
R
h
s
h
s
h
2
'
1
1
2
'




MIRROR
EQUATION
19

For this structure
A. The Radius R is positive and s’ is negative
B. The Radius R is negative and s’ is negative
C. R is positive and s’ is positive
D. 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’ (convex mirror)
22

Concept: Focal Length of a Mirror
23
f
s
s
s
R
s
s
1
'
1
1
2
R
s'
f
0)
(1/s
2
'
1
1










Going Backwards
24







'
0
'
1
)
2
(1/s
2
2
'
1
1
s
s
R
R
s
R
s
s

More Better – A Parabola
25
surveillance

Image Formation
26
0
'
0
0



s
R
s
‘
‘
y’<0
(from the diagram) so image is inverted.

The geometry……
27
s
s'
-
m
and
'
'
s
y
so
Triangles,
Similar
diagram)
in
image
inverted
from
sign
(-
'





s
y
y
y
m

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.
28
10 cm 5 cm
Normal to mirror
and bounces back
along incoming
path.
mm
y
s
s
m
s
f
R
s
s
4
5
.
'
5
.
7
'
1
2
'
1
1










the location and size of an 8mm object a distance 10 cm
from the mirror.
29
10 cm 5 cm
mm
y
s
s
m
cm
s
f
R
s
s
8
0
.
1
'
10
'
1
2
'
1
1










the location and size of an 8mm object a distance 2.5 cm
from the mirror.
30
10 cm 5 cm
eye
mm
y
s
s
m
cm
s
f
R
s
s
8
0
.
2
'
5
'
1
2
'
1
1









virtual
image

GEO1 (2).ppt

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