Classical Photography

1
The Interactions BetweenLight and MatterThe
Geometric Optics of Image FormationAlso called
"Ray Tracing"
2
(I) Clear Materials Bend Rays Light bending is
called "refraction".
ray
Air
Water
where a straight ray would come from.
where the ray really comes from.
3
Snells Law Describes the binding of light.
Bending of Light is called "Refraction"
The amount of bending depends on a property of
the material called "index of refraction", n.
Water n is low
Glass n is high
4
Snells Law The Angles and the Normal
Refraction (bending) is described by the change
in angle measured from the normal.
?1
The normal is an imaginary line perpendicular to
the surface.
?2
5
Snells Law The equations
Snells Law n1sin?1 n2sin?2
Define n 1 for a vacuum All other values of n
are gt1.
6
Refraction for Different Materials
light
45?
AIR
WATER
GLASS
DIAMOND
32?
28?
16?
7
Snells Law n1sin?1 n2sin?2 Examples
Material Index of Refraction, n Vacuum 1
(exactly) Air 1.0003 (approximately 1.000)
Water 1.33 Glass 1.5 Diamond 2.4
8
Snells Law n1sin?1 n2sin?2 It works exactly
the same in reverse.
Material 1
?1
n1
n2
?2
Material 2
Material Index of Refraction, n Vacuum 1
(exactly) Air 1.0003 (approximately 1.000)
Water 1.33 Glass 1.5 Diamond 2.4
9
Into and out of a flat plate of glass.
Glass n2 1.5
Air, n1 1.00
Air, n3 1.00
n1sin?1 n2sin?2
q4
q3
q2
q1
n3sin?3 n4sin?4
10
It can be shown that
q1 q4
q2 q3
and the input and output rays are parallel.
Glass n2 1.5
Air, n1 1.00
Air, n3 1.00
q4
q3
q2
q1
11
Trigonometry Review
RULES THAT DEFINE SIN, COS, TAN of an ANGLE
Hypotenuse (r)
Opposite Side (y)

• sin(?) y/r (opp/hyp)
• cos(?) x/r (adj/hyp)
• tan(?) y/x (opp/adj)

?
Adjacent Side (x)
12
(II) Refraction Is How Lenses Work
13
Using Refraction to Focus Light.
n11
n11
Glass Lens in Air
Parallel Rays
n21.5
Focal point of lens
Optical Axis
Focal length of lens, f
14
Parallel rays come to focus at one pointon the
image plane.
n11
n11
Glass Lens in Air
n21.5
Optical Axis
Parallel Rays different direction
Image Plane
Focal length of lens, f
15
A Chief Ray is a ray heading towardor away from
the center of the lens.
n11
n11
Glass Lens in Air
Examples of Chief Rays
n21.5
Optical Axis
Focal length of lens, f
16
Thin Lens ApproximationChief Rays pass through
the lens without deviation.
n11
n11
Glass Lens in Air
Examples of Chief Rays
n21.5
Optical Axis
Focal length of lens, f
17
(III) The Rules of Ray Tracing
18
We identify two types of very important rays
(A) Collimated Rays These are the rays that
enter or exit the lens parallel to the optical
axis. These rays pass through a focal point.
(B) Chief Rays These are the rays that go
through the center of the lens on the optical
axis. These rays are un-deviated.
19
Light from the object passes through the
lens. Follow the Ray Tracing Rule
Thin Lens
Object
Optical Axis
f
20
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21
This is how a projector works.
Object is a slide
h
Light Source
f
f
h'
22
Magnification The ratio of the size of the
image to the size of the object.
Magnification lt 1 in this example, so the image
is smaller than the object.
Object
Optical Axis
f
23
Traditional Ray Tracing Terms
Focal lengths for a thin lens in air f f'
Object
(collimated ray)
(chief ray)
h
h'
f'
f
L
L'
Object distance and height (L, h)
Image distance and height (L, h)
24
Try some different object locations, L. We
observe 6 special cases.
Object distance L Image distance L'
h
h'
f
f
25
NOTE this (chief) rays origin is the TIP of the
object (same as for the collimated ray)
26
Case (II) L between ? and 2f. As object moves to
the right, the image size increases.
h
h'
f
f
Image is real and inverted.
27
h
h'
f
f
28
Case (III) At L 2f, h h', and M 1.
h
h'
f
f
29
Case (IV) L between 2f and f, (a) the image is
still inverted, and (b) h' gt h, and M gt 1.
h' still increases as the object moves toward the
lens.
looks larger inverted
h
h'
f
f
30
For L between 2f and f, (a) the image is still
inverted, and (b) h' gt h, and M gt 1.
h' still increases as the object moves toward the
lens.
looks much larger inverted
h
f
f
h'
31
Case(V) L f. The rays are parallel.
They cross at infinity, so h' ? M.
This is the point of maximum confusion!
looks very confusing
h
f
f
32
Case (VI) L between f and the lens. The rays
diverge and look AS IF they come from an image
that (a) is erect and (b) enlarged, h'gth, m gt 1.
This is called a "virtual image".
We look through the lens, and it is a magnifying
glass!
h'
M gt 1
h
h
f
f
The rays diverge!!
33
This is how a magnifying glass works!
This is called a "virtual image".
We look through the lens, and it is a magnifying
glass!
h'
M gt 1
h
h
f
f
The rays diverge!!
34
Looks smaller and smaller as it nears the lens.
35
Case (VII) The image is at the lens, so L
0. The image is also at the lens, it is
erect, and it is the same size.
Object Image
f
f
36
Know and be able to ray trace the seven cases of
the thin, concave lens.
Object location (1) at infinity (2) gt 2f (3)
at 2f (4) between 2f and f (5) at f (6)
between f and the lens (7) at the lens
Know how h' and M change as the object
moves toward the lens and away from the lens.
37
(IV) Magnifying Power of a Lens
38
The ability of a lens to magnify an object is
determined by the focal length, f.
Lens 1
h
f
f
39
As f increases, the lens magnifies less. Long f
low magnifying power. Short f high magnifying
power.
Lens 2
h
f
f
40
Define the lens power, D 1/f If f is in
meters, then D is called the "diopter" of the
lens.
Lens 2
h
f
f
41
The "X" of the lens A practical measure of
magnifying power.
Without a lens, most people can focus
comfortably no closer than 23 cm from the object.
In focus for the average eye
h
do 23 cm
42
The "X" of the lens.
If we want to make the object look larger, we
move it closer to the eye. However, this makes it
out of focus to the eye.
h
distance d
43
The "X" of the lens.
In order to make the close object appear in
focus, we place a magnifying lens very close to
the eye. By trial and error, we find a lens that
will do this. Most people find that a lens with a
focal length, f, that is approximately equal to
the distance, x, works best.
h
distance d ? f
44
The "X" of the lens.
The object started out at distance do 23 cm.
The lens of focal length f allowed it to be in
focus at a distance of d f. In other words,
the lens brings the object closer by a factor of
do/d do/f 23/f. So, define the magnification
of the lens as X23/f.
h
h
do 23 cm
distance d ? f
45
The "X" of the lens.
For example, a lens of f 2.3cm allows most
people to move an object from 23 cm to 2.3 cm.
This makes the object appear 10 times as close.
Thus, we call the lens a 10X lens.
h
h
do 23 cm
distance d ? f
46
(V) Another Type of Lens
47
This kind of lens is called a "Convex Lens".
Object
f
48
This kind of lens is called a "Concave Lens".
f
F
It is possible to define focal points and ray
tracing for this kind of lens also, but that is
beyond the scope of this course.
Lens
49
(VI) When Things Go Wrong! Aberrations
50
The ideal lens focuses all rays from a single
object point onto a single image point.
Object
(A)
(B)
51
Aberration The failure of a lens to focus all the
rays at the same point.
Object
(A)
(B)
circle of confusion
52
Aberration The failure of a lens to focus all the
rays at the same point.
Object
(A)
(B)
circle of confusion and a blurred image
53
Dispersion The cause of one kind of
aberrationcalled chromatic aberration.

• Dispersion - Index of refraction, n, depends on
  the frequency (wavelength) of light.

Dispersion is responsible for the colors produced
by a prism red light bends less within the
prism, while blue light bends more.
54
Chromatic Aberration

• Dispersion results in a lens having different
  focal points for different wavelengths - this
  effect is called chromatic aberration.
• Results in a halo of colors.
• Solution Use 2 lenses of different shape and
  material (achromatic doublet).

White light
FRed
FBlue
Object (small dot)
Image with chromatic aberration
.
55
Spherical Aberration The shape of the lens has
to be ideal. However, it is easier and cheeper
to make lenses that are shaped like the surface
of a sphere.
A sphere is almost, but not quite exactly the
ideal shape.
F
Object (small dot)
Image with spherical aberration
.
56
Other Common Types of Aberration

• Coma
• Off axis blur that looks like the coma of a
  comet.
• Astigmatism
• Different focal lengths for different planes.
• Distortion
• Images formed out of shape.

.
.