Transcript chapter35

Chapter 35
The Laws of Geometric Optics
The Ray Approximation of Light in
Geometric Optics
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Geometric optics studies the
propagation of light.
Light travels in a straight-line path in a
uniform medium. Light changes its
direction when it meets the interface of
two media. Here reflection and
refraction take place.
Propagation of light in non-uniform
medium is not discussed here.
The ray approximation is used to
represent beams of light. Each ray is
represented as a line. The rays are
straight lines perpendicular to the wave
fronts
The path of light is reversible.
Reflection of Light
Specular reflection
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Reflection: a ray of light, the incident
ray, changes its direction at the
interface of two media, and travels
back in the same medium of the
incident ray.
Two types of reflection:
 Specular reflection: reflection from
a smooth surface. For parallel
incidence, the reflected rays are
parallel to each other.
 Diffuse reflection: reflection from a
rough surface. Reflected rays
travel in a variety of directions
even for parallel incidence.
We will only discuss specular
reflections here.
Medium 1
Medium 2
Diffuse reflection
Medium 1
Medium 2
Law of Reflection
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The incident angle and the
reflection angle.
 Incident angle: the angle ( 1 in
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the diagram) the incident ray
makes with the normal of the
interface at which the reflection
takes place.
Reflection angle: the angle
( 1' in the diagram) the reflected
ray makes with the normal of the
interface at which the reflection
takes place.
The Law of reflection:
  1
'
1
The incident ray, the reflected
ray and the normal are all in one
plane.
1'  1
Retroreflection
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Retroreflection: reflected
light travels in parallel but
opposite in direction to the
incident light.
Can be achieved by two
plane mirrors with an
angle of 90o between them.
Applications include
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Measuring the distance to
the Moon
Automobile taillights
Traffic signs
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One more example problem
The distance of a lightbulb from a large plane mirror is twice the distance of
a person from the same mirror. Light from the lightbulb reaches the person
by two paths. It travels to the mirror at an angle of incidence θ and reflects
from the mirror to the person. It also travels directly to the person without
reflecting off the mirror. The total distance traveled by the light in the first
case is twice the distance traveled by the light in the second case. Find the
angle θ.
Refraction of Light
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Refraction: When light enters from
one medium to the second, it
changes its direction in the second
medium. The angle the refracted
light makes with the normal (  2 in
the diagram) is called the angle of
refraction.
The incident ray, the reflected ray,
the refracted ray, and the normal all
lie in the same plane.
The reason for this bent is because
light travels at different speeds in
different medium:
sin 1 v1

sin  2 v2
Here v1 is the speed of light in
medium 1, v2 is the speed of light in
medium 2.
Medium 1
Medium 2
Snell’s Law of Refraction
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The index of refraction:
speed of light in vacuum c
n

speed of light in medium v
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Because the speed of light in any
material is less than its speed in
vacuum, index of refraction n  1
For a vacuum, n = 1
For air n = 1 is a very good
approximation.
For other media, n > 1
Snell’s Law of refraction
n1 sin 1  n2 sin 2
nair  1
nglass  1.52
Reflection and Refraction
1 
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1
2
1
2
Some Indices of Refraction
Frequency Between Media
When light travels from one
medium to another, its frequency
(and color) does not change (this
comes from energy conservation)
 Both the speed and the
wavelength do change
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From: v   f  , and f1  f 2
T
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One has:
1 v1
 
2 v2
c
n2
 , or n11  n2 2
c
n1
n2
c
Also from: v  f  , and n 
v
n1
We know that index of refraction is a (weak) function of frequency
(color). Different colors of light bent differently when refracted.
Variation of Index of Refraction with
Wavelength
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The index of refraction
for a material generally
decreases with
increasing wavelength
Violet light bends more
than red light when
passing into a refracting
material
Dispersion
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For a given material, the index of refraction
varies with the wavelength of the light
passing through the material
This dependence of n on  (in vacuum) is
called dispersion
Snell’s law indicates light of different
wavelengths is bent at different angles when
incident on a refracting material
Prism
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A ray of single-wavelength light
incident on the prism will emerge
at angle d from its original direction
of travel
 d is called the angle of deviation
 F is the apex angle
 The angle d can be expressed as a
function of the incident angle and
the apex angle.
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When a ray of white light (many
colors) enters a prism, the color
components are separated out into
a spectrum:
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Violet deviates the most
Red deviates the least
The remaining colors are in
between.
The Rainbow, a Nature’s show of
dispersion
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Sun light refracted/reflected
by rain drops has its color
components separated into
color spectrum.
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The angle between the
white light and the most
intense violet ray is 40°
The angle between the
white light and the most
intense red ray is 42°
Double Rainbow
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The secondary rainbow is
fainter than the primary
The colors are reversed
The secondary rainbow
arises from light that makes
two reflections from the
interior surface before
exiting the raindrop
Higher-order rainbows are
possible, but their intensity
is low
Total Internal Reflection
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When light travels from a medium
with larger index of refraction to a
medium with smaller n, as in the
diagram n1 > n2. The refracted angle
is larger than the incident angle.
As the incident angle increases to
the point that the refracted angle is
90o, this incident angle is called the
critical angle θc. Beyond it, there is
no refraction. All light is reflected
back and this phenomenon called
total internal reflection.
From Snell’s Law:
n1 sin c  n2
When medium 2 is air:
1
sin  c 
n
Diamond or glass?
You are cutting a diamond to
make it as brilliant as possible.
Find the critical angle for the
diamond in air.
What would be the cut angle for
flint glass ?
Fiber Optics
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An application of internal
reflection
Plastic or glass rods are
used to “pipe” light from
one place to another
Numerical aperture
Applications include
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Medical examination of
internal organs
Telecommunications
Fiber optics
What is the maximum
angle α that results in
total internal
reflection inside the
fiber optic cable? This
angle is usually called
the launching angle in
fiber optics.
Fiber Optics, cont.
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A flexible light pipe is
called an optical fiber
A bundle of parallel
fibers (shown) can be
used to construct an
optical transmission line
Construction of an Optical
Fiber
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The transparent core is
surrounded by cladding
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The cladding has a lower n
than the core
This allows the light in the
core to experience total
internal reflection
The combination is
surrounded by the
jacket