Transcript Properties of Light - FSU Physics Department

Chapter 31
Properties of Light
Summary of last lecture
Maxwell’s Equations
 → Electromagnetic waves
 Universal speed c = 3 x 108 m/s
 Electromagnetic Waves
 Gamma rays to radio waves
 Carry energy and momentum
 Exert pressure

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Topics
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
The Speed of Light

The Propagation of Light

Reflection, Refraction & Polarization

Sources of Light
Speed of Light
The first hint that
light traveled at
a finite speed
came from
measurements of
the period of
Jupiter’s moon Io
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Speed of Light
Ole Rømer’s Method (1675)
(Römer, Roemer)
When the Earth was at point C
the eclipses of Io were
observed to be later than
predicted by about 16.6 minutes
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Speed of Light
Rømer’s Method (1675)
Rømer reasoned that this must
be due to the time it takes
light to traverse the diameter
of the Earth’s orbit
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Speed of Light
Fizeau’s Method (1849)
The light was made to go through a gap
of the rotating toothed wheel and was
reflected back towards the wheel by
a mirror about
8.3 km away
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Speed of Light
Fizeau’s Method (1849)
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The angular speed of the wheel was
gradually increased until the travel
time of the light from the wheel to
the mirror and back
was equal to the
time between
successive
gaps
Speed of Light
Today, the speed of light is defined to be
exactly
c = 299792458 m/s
The meter is now defined to be the
distance traveled by light in vacuum in
1/299792458 s
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Speed of Light
Distances in astronomy are so great that
it is customary to use the distance traveled
by light in a given time as a distance unit
Examples – distance from Earth to:
1. Moon
1.25 light-seconds
2. Sun
8.33 light-minutes
3. Pluto
5.5 light-hours
4. Alpha Centauri 4.5 light-years (ly)
5. Andromeda
2.1 million ly
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The Propagation of
Light
The Propagation of Light
Huygens’ Principle
Each point on a wavefront serves
as a source of spherical
secondary wavelets,
whose envelope
forms the next
wavefront
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The Propagation of Light
Huygens’ Principle
Examples:
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Huygens’ Construction for
a Plane Wave
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At t = 0, the wave
front is indicated by
the plane AA’
The points are
representative sources
for the wavelets
After the wavelets
have moved a distance
cΔt, a new plane BB’
can be drawn tangent
to the wavefronts
Huygens’ Construction for
a Spherical Wave
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The inner arc
represents part of the
spherical wave
The points are
representative points
where wavelets are
propagated
The new wavefront is
tangent at each point
to the wavelet
The Propagation of Light
Fermat’s Principle
Light travels from one point
to another along the path of
least time
Note: The path of least time is not
necessarily the shortest path
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Reflection,
Refraction and
Polarization
Reflection & Refraction
The speed of light v in a transparent
medium is less than its speed c in
vacuum. Such media are characterized
by an index of refraction, n
c
n
v
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For water
For glass
n = 1.33
n = 1.5 to 1.66
Frequency Between Media

As light travels from one
medium to another, its
frequency does not change
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Both the wave speed and the
wavelength do change
The wavefronts do not pile
up, nor are created or
destroyed at the boundary,
so ƒ must stay the same
Reflection & Refraction
Law of Reflection: angle of reflection is
equal to angle of incidence
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Reflection & Refraction
Snell’s Law of Refraction
(Willebrord Snel van Royen, 1621)
n1 sin 1  n2 sin 2
Angle of
refraction
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Following the Reflected
and Refracted Rays
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Ray  is the incident
ray
Ray  is the reflected
ray
Ray  is refracted
into the lucite
Ray  is internally
reflected in the lucite
Ray  is refracted as
it enters the air from
the lucite
Example: Refraction from
Air to Water
n2 sin  2  n1 sin 1
 n1

 2  sin  sin 1 
 n2

0
 32.1
1
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Air:
Water:
n1
n2
1
=1
= 1.33
= 45o
Micro-Quiz
A material has an index of refraction that increases
continuously from top to bottom. Of the three paths
shown in the figure below, which path will a light ray
follow as it passes through the material?
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Micro-Quiz
As light travels from vacuum (n = 1)
to a medium such as glass (n > 1),
which of the following properties
remains the same:
(a) wavelength
(b) wave speed
(c) frequency
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Reflection & Refraction
As the angle of incidence is increased
a critical angle c is reached at which
the angle of refraction
is 90o.
n1 sin 1  n2 sin 90
n2
sin c 
n1
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0
Total internal Reflection
If the angle of incidence is > the critical
angle c there is no refracted ray and
all the light is reflected.
This is called total
internal reflection.
This requires
n1 > n 2
n2
sin c 
n1
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Fiber Optics
Light can be transmitted along transparent
glass fibers using total internal reflection.
Such fibers are used in imaging and
telecommunications
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Bending radii must
stay large enough
Reflection & Refraction
Mirages
These are caused by a continuous change
in the index of refraction of a medium,
which leads to
the gradual
bending of
light
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dispersion
Dispersion
The index of refraction depends slightly
on the wavelength. This causes light
comprising an admixture of wavelengths,
e.g., white light, to be
dispersed into
the different
wavelength
components
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Index of refraction vs
wavelength
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index of refraction for
a material usually
decreases with
increasing wavelength
Violet light refracts
more than red light
when passing from air
into a material
The Rainbow
 ray
of sunlight strikes a drop of
water in the atmosphere
 undergoes both reflection and
refraction
 refraction
at the front of the drop:
• nv > nr  violet light will deviate the
most
• Red light will deviate the least
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Rainbow
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Reflection inside drop at
the back surface -- back
towards front
Then again refraction on
leaving drop into the air
Net angle of deviation
depends on color
 violet ray deviates by
40° wrt original direction
of sunlight
 red ray by 42°
Observing the Rainbow
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Observer sees red ray from drop higher
up
violet light to the observer appears to
come from lower parts of rainbow
other colors of the spectrum are between
the red and the violet
Polarization
We noted in a previous lecture that an
electromagnetic wave travels in a direction
perpendicular to its electric field.
y
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z
x
Polarization
If the direction of the electric field
is constant as the wave propagates,
the latter is said to be linearly polarized
y
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z
x
Polarization
Polarization by Absorption
A polarizer is a device that allows only
waves of a given
polarization
through.
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Polarization
Polarization by Absorption
If the angle between two polarizers
is  then the
intensity of
light through the
analyzer is given
by the law of
Malus
2
I  I 0 cos 
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Polarization
 Light
can be polarized in
other ways:
 Reflection
 Scattering
 Birefringence
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Sources of Light
Continuous
spectrum
Hydrogen
Helium
Barium
Mercury
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See http://astro.ustrasbg.fr/~koppen/discharge/ for more spectra
Summary
Speed of light in vacuum
c = 299792458 m/s (def. of meter)
 Huygens’ principle
 in medium m: cm < c,
refractive index nm = c/cm
 Reflection and refraction
at media boundary
 Snell’s law
n1 sin 1  n2 sin 2
 total internal reflection
 dispersion: n varies with wavelength
 polarization by absorption, reflection,
birefringence
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