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The “normal” is an
imaginary line perpendicular
to the interface (surface).
We measure everything
from that.
inci
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t
ligh
ht
d lig
cte
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refl
A “ray” illustrates the
path of a light wave.
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Fig. 33-16
Fig. 33-16
Refraction
Light travels more slowly through a material — gas,
liquid, or solid — than it does through a vacuum. We
denote the speed of light in a vacuum as c, and the
speed of light in some material as v.
The ratio n = c/v is called the index of refraction
(a.k.a. the refractive index).
v ≤ c so n ≥ 1.
n has no units.
Larger refractive index (higher n) means slower
speed of light (lower v).
n depends on material, and on wavelength (!).
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Laws of Reflection and Refraction
Rules describing the
behaviour of light when it
encounters an interface
between two media.
Incident, reflected, and
refracted rays are all in the
same plane.
Law of Reflection:
The angle of reflection is the
same as the angle of
incidence: θ’1 = θ1.
Fig. 33-16
Law of Refraction
(“Snell’s Law”):
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Snell’s Law:
e.g.: Reflection & Refraction
n1 = 1.33
n2 = 1.77
θ2 = ???
θ3 = ???
Fig. 33-17
Example: Water and Glass
A laser is fired at the surface of
some water at an angle of
θi = π/3 (60º).
Air
na = 1.00
θi
It passes through the water and
into the glass bottom of the
container, then out into the air.
Water
nw = 1.33
What are θw, θg, and θf?
Glass
ng = 1.52
Air
na = 1.00
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θw
θw
Light Waves and Refraction
When light goes from one medium to another, the
frequency of that light doesn’t change.
• You get the same number of waves leaving an
•
interface in a given amount of time as you have
entering.
Waves don’t stop, and they aren’t created or destroyed
at the interface.
v = λf, and the frequency doesn’t change, so
the wavelength must change if v is different.
θg θg
f1 = f2
θf
!
v1/λ1 = v2/λ2. Since v = c/n, we get:
! n1 λ1 = n2 λ2.
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Total Internal Reflection
When a light ray goes from a
“slower” medium to a “faster”
medium (na > nb) —"for
example, from water or glass
into air —"the ray bends away
from the normal, as we’ve seen.
•
If θa = 90° (“normal
incidence”), θb = 90°.
•
After that, nb< na means
θb > θa.
Remember, there’s always a
reflected ray as well.
•
You might not notice it if
most of the light passes into
the new medium.
n b< n a
na
θb
θb
We can determine the critical angle from Snell’s Law:
θb = 90°
θa
θa
θa
θ’a = θa
Note that this only works when you’re going from a
slower medium to a faster medium (higher to lower n).
Go the other way and light at any incident angle refracts.
θa = θcrit
•θ
= θcrit when θb = 90°, so sinθb = 1.
Then na sinθcrit = nb, or
! sinθcrit = nb/na
Eventually θb = 90º...
The outgoing light ray will be directed
along the surface!
Snell’s law breaks down after that —"no
more refraction!
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Applications
Optic fibers
• Communication (denser data transmission, less
noise)
• Endoscopes (for looking around inside the body)
Light guides
• Particle physics
• Natural lighting in buildings
Jewelery
•
a
A diamond’s brilliance is due to total internal
reflection on the back surface.
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Chromatic Dispersion
“chroma” means “colour”
The speed of light in a material
depends on the light’s wavelength (or
frequency). Light is weird!
For most (but not all!) materials, the
speed of light increases (smaller n)
with increasing wavelength.
•
The light is “dispersed”
—"different wavelengths
(different colours!) travel at
different speeds.
•
Different colours bend differently
when crossing interfaces
(different n in Snell’s law).
n vs λ for fused quartz
more
bending
less
bending
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http://xkcd.com/964/
Rainbows:"how do they work?
Double reflections
! double rainbow!
Fig. 33-21
Polarization by Reflection
Polarization by Reflection
When unpolarized light strikes a surface, the
reflection can be partially or even entirely polarized.
• How much it’s polarized depends on the
angle of incidence.
The plane of incidence is the plane defined by the
incident, reflected, and refracted rays. (It’s always
perpendicular to the surface.)
Components perpendicular to this plane tend to reflect
more strongly than components parallel to this plane.
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The Polarizing Angle
Amount of polarization depends on the incident angle
(and the materials involved).
Sir David Brewster, in 1812, found
experimentally that, when the
incident light is at the "polarizing
angle", the reflected and refracted rays
are at right angles to each other.
For one specific angle, only the parallel component
reflects.
This means that, in the diagram,
θB + π/2 + θr= π, or
!
θB = (π/2 - θr).
•
The Law of Refraction (Snell’s Law)
tells us that n1 sinθB = n2 sinθr.
The perpendicular component is all refracted
(along with some parallel component).
So at this angle, the reflected light is 100% polarized!
The incident angle at which this happens is called the
polarizing angle.
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Example:
Reflections on
Water
Consider the surface of an
unoccupied swimming pool. In the
day, light reflects from the surface;
at night, underwater floodlights are
turned on and the light comes up
from below.
For both day and night:
(a) what is the polarizing angle?
(b) what is the angle of refraction
for the transmitted part of the
light when we’re at the polarizing
angle?
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90°
But sinθB = sin(π/2 - θr) = cosθr.
(Think of graphs of sin and cos!)
Plug into Snell’s Law and rearrange:
Brewser’s Law for the polarizing angle.
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