Geometric Optics
Light What is light? Waves or particles?
Geometric optics: light travels in straight-line paths called rays
This is true if typical distances are much larger than the wavelength
Geometric Optics
both
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What it is about Phenomena addressed by geometric optics:
Propagation: light goes in straight lines
Reflection: angle of incidence = angle of reflection
Refraction: Snell’s law
Phenomena not addressed by geometric optics:
Polarization
Diffraction
Interference
Photoelectric effect
Geometric Optics 3
Electromagnetic theory
Quantum mechanics
Reflection and Refraction
Geometric Optics
a
r
ba
r
b
incident angle
reflection angle
refraction angle
medium a (e.g. air)
medium b (e.g. glass)
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The incident, reflected, and refracted rays, and the normal to the surface, all lie in the same plane
Specular and Diffusive Reflection
Geometric Optics
specular reflection: smooth interface, definite reflection angle
diffusive reflection: rough interface, scattered reflection
we’ll discuss this one
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Image
Geometric Optics
P 'P
mirror
object point image point
Object point: where the rays actually come from Image point: where the rays appear to come from
s
s: object distance s’: image distance
's
here outgoing rays do not actually come from P’ image is virtual if they did, the image would be real
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Sign Rules for Distances
Geometric Optics
P 'P mirror
object point image point
0s 0's Object distance: when the object is on the same side as the incoming light, s>0, otherwise, s<0
Image distance: when the image is on the same side as the outgoing light, s’>0, otherwise, s’<0
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Sign Rules for Distances
Geometric Optics
P 'Pobject point image point
0s
0's
Object distance: when the object is on the same side as the incoming light, s>0, otherwise, s<0
Image distance: when the image is on the same side as the outgoing light, s’>0, otherwise, s’<0
refracting interface
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Lateral Magnification
Geometric Optics
mirror:
object image
s 's
y 'yP 'P
Q 'Q
need at least two points (P,Q) to figure it out
y
ym
'
1
'
m
ss
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Inverted and Reversed Images Image can be erect (right side up) or inverted (upside
down)
Image can be reversed (“mirror-image” – left hand looks like right and vice versa)
Geometric Optics
hole
mirror camera obscura
a plain mirror image is virtual, erect, and reversed
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Reflection in a Sphere
Geometric Optics
P 'PC
B
R
h
s
h
s
h
tan
'tan
tan
's
R
h
s
Equations are involved
s’ depends on α
V
11
Reflection in a Sphere
Geometric Optics
P 'PC
B
R
h
s
h
s
h
tan
'tan
tan
's
R
h
s
Use paraxial approximation
V
12
Spherical Mirror Reflection
Geometric Optics
P 'P
Rss
2
'
11
no α dependence!
's
s
13
Focal Point
Geometric Optics
P
F
fR
s
Rs
2'
2
'
11
focal length
object is far away to the left
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Focal Point
Geometric Optics
F
fR
s
Rs
2
211
works in both ways
object is placed in the focal point
These things are approximately true for spherical mirrors. They are exactly true for parabolic mirrors.
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Spherical Mirror: s>f
Geometric Optics
P 'P
fss
1
'
11
f
s
's
F
0'
s
fs
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Spherical Mirror: s<f
Geometric Optics
P 'P
fss
1
'
11
f
s
's
F
0'
s
fsimage is virtual
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Spherical Mirror Magnification
Geometric Optics
P C
's
R
s
Q
'QV
'Py
'y
s
s
y
ym
''
because triangles PQV and P’Q’V are similar
s’>0: image is real and inverted (m<0) s’<0: image is virtual and erect (m>0)
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P 'P
Convex Spherical Mirror convex = curving out
All is exactly the same except that f (and R) is negative
Geometric Optics
'ss
P 'P
'ss
convex concave
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Focal Point of Convex Mirror
Geometric Optics
F
focus is virtual
provided s>0, a convex mirror always forms a virtual, erect, reversed image (same as the plain mirror) m=1 for plain mirror m<1 for convex mirror
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Principal rays Need them to find image position and magnification
Geometric Optics Geometric Optics
P C
Q
V'P
'Q
F
B
A
QBQ’: ray parallel to the axis reflects through focal point
QAQ’: ray through focal point reflects parallel to the axis
QCQ’: ray through the center reflects back
QVQ’: ray to the vertex forms equal angles with the axis
this construction neglects aberrations
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Snell’s law
Geometric Optics 22
bbaa nn sinsin a b
medium a (e.g. air)
medium b (e.g. glass)
This is the basic law of refraction
angle of incidence not equal to angle of refraction!
n: index of refraction what is this?
bnan
Index of Refraction = ratio of the speed of light in the material to that in
vacuum
Geometric Optics
v
cn
n>1: light travels slower in the material than in vacuum
What changes when the light passes from one medium to another? * Frequency ? No, it would imply creating/destroying waves * Speed? Yes, because the media have different n * Wavelength? Yes, because λ=v/f
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Total Internal Reflection Snell’s law may give sinθ>1 – what does it mean?
Geometric Optics 24
Cba nn sin
critical angle
can only happen if ba nn
There are always two rays: reflected and refracted
At some angle, the refracted ray disappears
bnan
Fiber Optics Light can be transmitted along a fiber with almost no
loss due to total internal reflection
Due to impurity of glass, the signal eventually degrades (typical rates are ~50%/km)
Geometric Optics 25
Widely used in communications – much higher frequency than for regular wires, therefore can transmit much more data
Refraction at a Sphere
Geometric Optics
P
B
R
h
s
h
s
h
b
a
tan
'tan
tan
's
h
s
V C
a
b
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Refraction at a Sphere
Geometric Optics
P
B
R
h
s
h
s
h
b
a
tan
'tan
tan
's
h
s
V C
a
b
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Refraction at a Sphere Use Snell’s law
Geometric Optics
)()(
ba
b
a
nn
R
nn
s
n
s
n abba
'
sn
snm
b
a 'magnification:
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bbaa nn sinsin
Thin Lens Lens = an optical system with two refracting surfaces
Geometric Optics
P 'P
1s
'2s
'1s2s
Thin lens:
'12 ss
bnan
1R
2R
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Thin Lens Equation
Geometric Optics
222111 ',
' R
nn
s
n
s
n
R
nn
s
n
s
n baababba
',,1 12 ssnnn ba assumptions:
fRRn
ss
111)1(
'
11
2121
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Lens Types
Geometric Optics
021 RR02
1
R
R12 0 RR 021 RR
02
1
R
R21 0 RR
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Graphical Methods for Lenses Be careful with the focal length sign!
Geometric Optics 32
Graphical Methods for Lenses
Geometric Optics 33