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PH 222-2A Spring 2015
Images
Lectures 24-25
Chapter 34
(Halliday/Resnick/Walker, Fundamentals of Physics 9th edition)
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Chapter 34
Images
One of the most important uses of the basic laws governing light is the
production of images. Images are critical to a variety of fields and industries
ranging from entertainment, to security, to medicine.
In this chapter we define and classify images, and then classify several basic
ways in which they can be produced.
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Two Types of Images
real image
object
lens
object
mirror
virtual image
Image: A reproduction derived from light.
Real Image: Light rays actually pass through image, really exist in space (or on
a screen for example) whether you are looking or not.
Virtual Image: No light rays actually pass through image. Only appear to be
coming from image. Image only exists when rays are traced back to perceived
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location of source.
A Common Mirage
Light travels faster through warm air  warmer air has smaller index of
refraction than colder air  refraction of light near hot surfaces.
For observer in car, light appears to be coming from the road top ahead, but is
really coming from the sky.
Fig. 34-1
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Plane Mirrors, Point Object
Plane mirror is a flat reflecting surface.
Identical triangles
Fig. 34-2
Ib  Ob
Fig. 34-3
Plane Mirror:
i  p
Since I is a virtual image, i < 0.
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Plane Mirrors, Extended Object
Each point source of light in the
extended object is mapped to a
point in the image.
Fig. 34-4
Fig. 34-5
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Plane Mirrors, Mirror Maze
Your eye traces incoming rays straight
back, and cannot know that the rays may
have actually been reflected many times.
1
2 8
7
9
3 6
1
2
4
5
3
4
5
6
7
8
9
Fig. 34-6
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plane
concave
convex
Fig. 34-7
Spherical Mirrors, Making a Spherical Mirror
Plane mirror  concave mirror
1. Center of curvature C:
in front at infinity  in front but closer
2. Field of view - the extent of the scene that is reflected to observer
wide  smaller
3. Image
i=p  |i|>p
4. Image height
image height = object height  image height > object height
Plane mirror  convex mirror
1. Center of curvature C:
in front at infinity  behind mirror and closer
2. Field of view
wide  larger
3. Image
i=p  |i|<p
4. Image height
image height = object height  image height < object height
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Spherical Mirrors, Focal Points of Spherical Mirrors
concave
convex
Fig. 34-8
1
Spherical Mirror: f  r
2
r > 0 for concave (real focal point)
r < 0 for convex (virtual focal point)
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Images from Spherical Mirrors
Start with rays leaving a point on object, where they intersect, or appear to
intersect, marks the corresponding point on the image.
Fig. 34-9
Real images form on the side where the object is located (side to which light is
going). Virtual images form on the opposite side.
1 1 1
 
Spherical Mirror:
p i f
h'
Lateral Magnification: m 
h
i
Lateral Magnification: m  
p
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Locating Images by Drawing Rays
Fig. 34-10
1.
2.
3.
4.
A ray that is parallel to central axis reflects through F.
A ray that reflects from mirror after passing through F emerges parallel to central axis.
A ray that reflects from mirror after passing through C returns along itself.
A ray that reflects from mirror after passing through c is reflected symmetrically about the
central axis.
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Proof of the Magnification Equation
Similar triangles (are angles same?)
Fig. 34-10
de cd

ab ca
i
m
p
de
cd  i, ca  p,
 m
ab
(magnification)
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The Spherical Mirror Formula
     and     2
Fig. 34-20
1
                 2
2
ac ac
ac ac

 , 

cO p
cC r
ac ac


CI
i
1
f  r r 2f
2
ac ac
ac
1 1 1

2
  
p
i
2f
p i f
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Spherical Refracting Surfaces
Fig. 34-11
Real images form on the side of a refracting surface that is opposite the object (side to
which light is going). Virtual images form on the same side as the object.
Spherical Refracting Surface:
n1 n2 n2  n1
 
p i
r
When object faces a convex refracting surface r is positive. When it faces a concave
surface, r is negative. CAUTION: This is reverse of mirror sign convention!
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Thin Lenses
Converging lens
Diverging lens
Fig. 34-13
Thin Lens:
1 1 1
 
f
p i
1 1
1
Thin Lens in Air:
  n  1   
f
 r1 r2 
Lens only can function if the index of the lens is
different from that of its surrounding medium.
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Images from Thin Lenses
Fig. 34-14
Real images form on the side of a lens that is opposite the object (side to which light is
going). Virtual images form on the same side as the object.
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Locating Images of Extended Objects by Drawing Rays
Fig. 34-15
1. A ray initially parallel to central axis will pass through F2.
2. A ray that initially passes through F1, will emerge parallel to central axis.
3. A ray that initially is directed toward the center of the lens will emerge from the lens
with no change in its direction (the two sides of the lens at the center are almost
parallel).
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Image formation by a converging lens
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Two-Lens System
i1
p2
i2
O
p1
I1
Lens 1 O2
I2
Lens 2
1. Let p1 be the distance of object O from Lens 1. Use equation and/or
principle rays to determine the distance to the image of Lens 1, i1.
2. Ignore Lens 1, and use I1 as the object O2. If O2 is located beyond Lens 2,
then use a negative object distance p2. Determine i2 using the equation
and/or principle rays to locate the final image I2.
The net magnification is: M  m1m2
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Two converging lenses, each with a focal length of 0.12 m, are used in combination to
form an image of an object located 0.36 m to the left of the left lens in the pair. The
distance between the lenses is 0.24 m.
(a)Where is the final image located relative to the lens on the right?
(b) What is the total magnification of the lens combination?
0.24m i2
p2
p1
i1
a ) fin d im a g e d is ta n c e i 1 o f th e firs t o b je c t
1
1
1
1
1
1
p  f1





 1
p 1 i1
f1
i1
f1
p1
p1  f1
 i1 
p1  f1
0 .3 6  0 .1 2
0 .3 6  0 .1 2


 0 .1 8 m
p1  f1
0 .3 6  0 .1 2
0 .1 8
p 2  0 .2 4  i1  0 .2 4  0 .1 8  0 .0 6 m
fin d im a g e d is ta n c e i 1 o f th e s e c o n d o b je c t
p  f2
1
1
1
0 .0 6  0 .1 2
0 .0 6  0 .1 2


 i2  2


  0 .1 2 m
p2
i2
f2
p2  f2
0 .0 6  0 .1 2
 0 .0 6
 im a g e is lo c a te d 0 .1 2 m to th e le ft o f th e rig h t le n s
 i   i 
b ) M  m1  m 2    1     2  
 p1   p 2 
T h e s iz e o f th e fin a l im a g e = s iz e o f
 0 .1 8    0 .1 2 


  1
0 .0 6 
 0 .3 6  
th e o b je c t, b u t th e im a g e is in v e rte d .
The human eye
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The refractive power of a lens. The diopter.
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Focal point of contact lens
Contact lens should bring the image of the object positioned at the near
point of normal eye (0.25m) to the near point of farsighted eye (0.80m).
=+0.36 m; refractive power = 1/0.36 m = 2.75 Diopters
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Optical Instruments, Simple Magnifying Lens
You can make an object appear
larger (greater angular magnification)
by simply bringing it closer to your
eye. However, the eye cannot focus
on objects closer than the near point:
pn~25 cmBIG & BLURRY IMAGE
A simple magnifying lens allows the
object to be placed close by making a
large virtual image that is far away.
25 cm
Simple Magnifier: m 
f
Fig. 34-17
Object at F1
'
m 

h
h

and  ' 
25 cm
f
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Problem 93. Someone with a near point Pn of 25 cm views a thimble through a simple magnifying
lens of focal lengths 10 cm by placing the lens near the eye. What is the angular magnification of
the thimble if it is positioned so that its image appears at: a) Pn; b)infinity?
a) Without the magnifier, q = h/Pn . With the
magnifier, letting
i = – |i| = – Pn, and we obtain
1 1 1 1 1 1 1
      .
p f i f i
f Pn
Consequently,
1 1 1 1 1 1 1
      .
p f i f i
f Pn
m 
  h / p 1 / f  1 / Pn
P
25 cm


 1 n  1
.
 h / Pn
1 / Pn
f
f
In the case where the image appears at infinity, let i   | i |  so that
m 
  h / p 1/ f Pn 25 cm
.




 h / Pn 1/ Pn f
f
With f = 10 cm,
1/ p  1/ i  1/ p  1/ f
m 
we have
25 cm
 2.5.
10 cm
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Optical Instruments, Compound Microscope
O close to F1
I close to F1’
Mag. Lens
Fig. 34-18
m
i
s

p
f ob
since i  s and p  f ob
s 25 cm
M  mm  
f ob f ey
magnification compounded (microscope)
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Optical Instruments, Refracting Telescope
I close to F2
and F1’
Mag. Lens
Fig. 34-19
 ey
h'
h'
m  
,  ob 
,  ey 
 ob
f ob
f ey
f ob
 m  
f ey
(telescope)
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