THE SPEED OF LIGHT AND
HOW LIGHT PROPAGATES
Purdue University – Physics 241 – Lecture 21
Brendan Sullivan
Overview


Attempts to measure the speed of light & current
definition of the speed of light
How light propagates
 Photons
& Wave-Particle Duality
 Huygens Construction
 Fermat’s Principle

Reflection and Refraction at interfaces
 How
light changes outside of vacuum
History of the speed of light


Prior to 17th century we thought
the speed of light must be infinite
Galileo: put a mirror very far
away and see how long it takes
for light to return
too fast to measure, but he
did see some delay
d
 Returned

Fizeau: Use a cog to set limits on
the speed of light
t
r
c
2d
c
Determining the speed of light from
Jupiter’s moon Io



1675: Ole Romer determines approximately the
speed of light by studying eclipses of Io
By comparing the path length difference and the
duration of the eclipse, we can estimate the speed
of light
Found the eclipse started about 15s later than
predicted; not very accurate measurement but good
for an order of magnitude
c
r
t
The definition of the speed of light

Lecture yesterday (from solving the wave equation):
c
1
299,792,458m / s 3 108 m / s
0 0



Today, we define the meter as how far light will
travel in 1/299792458th of a second
This is the speed of light in vacuum; we’ll find out
later how it changes in a medium
The light year (ly) is the distance that light will
travel in 1 year
A
parsec is around 3.26 ly
Huygen’s Construction



Describes how light propagates
Was originally just an empirical description,
Kirchhoff later showed the wave equation recovers
Huygen’s Construction
Each point on a primary wavefront serves as the
source of spherical secondary wavelets. The
primary wavefront later is the envelope of these
wavelets.
http://home.hiroshimau.ac.jp/atoda/Huygens_principle.gif
Fermat’s Principle

Light traveling from point A to B will take the path
which minimizes the travel time.
 This
may not be the shortest spatial path
 Much like driving on an expressway; it may be a little
out of the way, but you can drive faster

We can use this to derive the laws of reflection and
refraction
The index of refraction describes how
the speed of light changes in materials

In materials, light slows down by a factor n, the index of refraction
v


c
n
If the velocity changes, the wavelength also changes (not the
frequency)
c
0
v
f0
n n
Light passing through a material (e.g. water with n=1.33) does not
change colors
Quiz Question 1
We need to send an urgent message to the
International Space Station!! If we send the
message via radiowaves (EM waves), how long will
it take to get there? The space station 460km from
Earth.
a) Instantaneously
b) 1.5ms
c) 3.0ms
d) 0.75ms
e) >1s
At an interface, some light is reflected
back and some refracts inwards
Law of Reflection: Light reflects back at the same angle
1
'
1
2
Snell’s Law: Light bends when it enters a new medium (refractive index)
1
'
1
n1
n2
n1 sin( 1 )
n2 sin( 2 )
Total internal reflection




n1
sin ( sin( 1 ))
n2
Snell’s Law: n1 sin( 1 ) n2 sin( 2 )
2
n1
What if sin( 1 ) 1 ?
n2
We observe no wave leaving the medium!
Critical angle: sin( C ) n2
1
 At
n1
any angle greater than or equal to the critical, we
observe TIR

This is the basis of fiber optic cables
medium 2
medium 1
The “fish eye” effect can be attributed
to total internal reflection


The fish eye effect is a result of evanescent field of
light refracting at the air-water interface
See example 31-5 in text book
Photo: http://microsites.lomography.com/holga/content/galleries/full-fisheye/fisheye_7.jpg
Dispersion refers to an n value that
depends on the wavelength

In dispersive materials, n becomes n(λ) or n(f)
 This
also means that different color light travels at
different speeds


This is how prisms work, rainbows are formed, and
has some industrial applications
White light is a result of adding all the colors of
light
Dispersion gives rise to rainbows


Water droplets are slightly dispersive, which is why
rainbows display the spectrum they do
Descartes showed that a rainbow is best viewed at
42 degrees with respect to the sun line
water
droplet
 red is outside.
 intensity
max at 42O
rainbow
Quiz Question 2

Which of the following rays is drawn incorrectly if
n1<n2?
C
A
1
2
1
n1
B
n2
D) All of the rays are drawn correctly
Mirages are caused by gradual spatial
changes in the index of refraction




On a hot day, exposed rocks,
pavement, and sand get
really hot
Air near these hot surfaces is
less dense, which light can
travel through slightly faster
(change in n)
This continuous n causes a
“continuous version” of Snell’s
Law (refraction) to occur
The result is mirages
Today will be 100°F. Think you can
find a road mirage?
Cloaking devices work by rerouting EM
waves using varying n values

One (basic) idea for cloaking is to have EM waves
wrap around the cloaked object (left)


Like a mirage, but transmitting EM information from behind
the object
Applications: Cloaking people, machines, and sending
undetectable transmissions
http://www.universetoday.com/wpcontent/uploads/2008/08/cloaking.jpg
http://3quarksdaily.blogs.com/3quarksdaily/i
mages/image006_3.gif