Transcript L11:Geometric optics (Ch. 33)

Lecture 11
Geometric optics
Physics 114
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Lecture XI
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Principles of geometric optics
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Concepts
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Ray model of light
Image formation
Reflection
Refraction
Dispersion
Total internal reflection
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EM waves
• c – speed of light (m/s)
• f – frequency (Hz=1/s)
 l – wavelength (m)
 
EB
 
E v
 
Bv
c  fl
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Ray model of light
• Light is an EM wave diffraction (go around
obstacles)
• This happens on microscopic scale
• In everyday life we use straight line approximation
for light propagation = Ray model of light 
geometric optics
• We infer positions of objects assuming light travels
in straight lines.
Geometry is important,
Bring ruler and pencil,
make good pictures!!!
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Reflection
• We see objects because
– They emit light (Sun, light bulb)
– They reflect light (Moon, table)
• angle of incidence = angle of
reflection:
qi=qr
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Rough
surface
Lecture XI
Polished surface.
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Formation of image
• Eye assumes light
propagates in straight
lines  image (rays
of light crossing) is
formed behind the
mirror
• do – distance to object
• di – distance to image
• For plane mirror
do= di
No light here
 Virtual image
If light actually goes through the place
where image is formed  real image
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Spherical mirrors
• Convex mirror bulges out – diverges light
• Concave mirror caves in – converges light
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Focus
• Parallel beam of light (e.g. from a very distant object) is
converged in 1 point – focal point F
• Distance from the mirror to F is called focal distance, or
focus
f =r/2
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Ray tracing
3 Easy rays:
1. Parallel  through focus
2. Through focus  parallel
(reversible rays)
3. Through the center of
curvature C  itself
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Magnification
• h0 – object height
– h0>0 - always
• hi – image height
– hi>0 – upright image
– hi<0 – inverted image
• m=hi/h0 - magnification
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hi
di
m

ho
do
|m|>1 –image larger than object
|m|<1 –image smaller than object
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Mirror equation
• d0 – distance to object
– d0>0 - always
• di – distance to image
1 1 1
 
do di
f
– di>0 – real image
– di<0 – virtual image
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Convex mirror
• Virtual focus – parallel
beam focuses behind the
mirror:
f<0
• Same rules for ray
tracing.
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Sign convention for mirrors
d0>0
h0>0
di>0 – real image
hi>0 – upright image
f>0 – concave mirror
hi
di
m

ho
do
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di<0 - virtual image
hi<0 - inverted image
f<0 – convex mirror
•hi>0di<0 – upright image is always virtual
•hi<0di>0 – inverted image is always real
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Images in curved mirrors
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Concave mirror
d0>r – (real, inverted), smaller
r>d0>f – (real, inverted), larger
d0<f – (virtual, upright), larger
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• Convex mirror
• Image is always
(virtual, upright), smaller.
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Speed of light in medium
• Speed of light in vacuum:
c=3.0x108m/s
• Speed of light in media:
v<c
• Index of refraction:
n=c/v >1.0
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From table 33-1
Vacuum
n=1.00
Air
n=1.0003
Water
n=1.33
Diamond
n=2.42
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Refraction
• The front is
slowing
down
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Refraction, Snell’s law
n1 sin q1  n2 sin q 2
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n1
sin q 2  sin q1
n2
n2  n1  q 2  q1 Bend toward normal
n2  n1  q 2  q1 Bend away from normal
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Image formation
• Eye still assumes light
propagates in straight lines
 optical illusions
– Image is shifted
– Pool appears shallower
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What if n depends on l?
• If n depends on l  angle of refraction depends on l
• n(red)<n(green)
1. A-red, B-green
2. B- red, A-green
A
B
Dispersion
This is why rainbow occurs
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Total internal reflection
n2
sin q 2  sin q1
n1
n1  n2
sin q 2  1
For q>qc - total internal reflection –
no light come out – all light is reflected
Fiber optics
Necessary condition:
from thick to thin media
n2
sin q c 
n1
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1.3 m
2.1 m
2.7 m
x
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