Download •How vision works •What is light •Wavelength and Frequency: c = f λ

Lecture 2 – Chapter 1
Homework due next week; see course website
Go to physics.colorado.edu, and select:
-> programs of study -> undergraduate -> physics courses
-> Course Home Pages -> Phys 1230 (web page)
We are
here
•How vision works
•What is light
•Wavelength and Frequency: c = f λ
Scientific notation and metric units
Electromagnetic spectrum
•Speed of light
•Amplitude
•Direction
Rays and wavefronts
•Polarization
•Phase difference
Ch. 1: How vision works
Light from a source travels to the eye, OR
Light from a source is reflected or scattered toward the eye.
The sun is self-luminous.
The moon shines by scattered light.
Reflection in a mirror is a kind of scattering with a special
direction (more later).
Surface scattering: how we see pages of a book. Light
leaves in all directions.
Volume scattering: how we see fog, clouds, blue sky.
Transparent: no scattering.
1
What is light?
Light is an electromagnetic wave.
(uhh...what is electromagnetic? what is a wave?)
λ is the wavelength or distance between crests.
side view
end view
Blue arrow is electric field direction and amplitude,
red arrow is magnetic field direction and amplitude.
Electric fields make charges “q” move, creating a current.
The current can be in your optic nerve, or a solar cell.
What is “electromagnetic”?
The electromagnetic force is one of 4 fundamental forces.
The electromagnetic force includes:
• the electric force
• the magnetic force
The unification of the theories of the electric and magnetic forces into
a single (beautiful and elegant) theory of electromagnetism is one of
the great triumphs of physics.
The unification of different theories results in overall simplification
and increased understanding.
2
The fundamental forces (interactions)
celestial
terrestrial
In the future?
1. gravitational
electric
magnetic
2. electromagnetic
electroweak
3. weak
GUT
(Grand
Unified
Theory)
Theory of
Everything
4. strong
The unification of terrestrial and celestial gravity
(thanks to Isaac Newton)
The force that keeps the moon orbiting the earth is the same as the force that
makes bricks fall to the floor.
This is not at all obvious, though it is now very familiar.
People used to think that the moon was pushed (e.g., by angels) around the
earth. Newton realized that the moon doesn’t need to be pushed forward
around the earth; it tends naturally to move forward. To stay in orbit, the moon
needs to be pulled toward the earth. Conclusion: the moon and bricks are both
pulled toward the earth by gravitational attraction.
3
The unification of electric and magnetic forces
(thanks to James Maxwell, with help)
The electric force: a charge produces an electric field which acts upon another charge
force of charge q1 on charge q2:
Fe = k
q1q2
d2
d
q1
q2
constant that reflects how strong the electric force is
The magnetic force: a current (moving charge) creates a magnetic field which acts
upon other moving charges
force of wire 1 carrying current I1
on wire 2 carrying current I2:
Fm = h
I1 I 2
l
d
l
d
constant that reflects how strong the magnetic force is
I1
I2
(Notice symmetry between 1 and 2? Newton’s 3rd Law.)
Key insight leading to electromagnetic unification
(thanks to Michael Faraday)
Faraday showed: a changing magnetic field can create an electric field.
(aside: this is how electric generators work--they move a magnet near a
wire; moving the magnetic varies the magnetic field, creating an electric
field, which moves electrons in the wire).
Have you noticed symmetry in physics? For example, the force of object A
on object B equals the force of object B on object A (Newton’s 3rd Law).
Maxwell suggested that perhaps a changing electric field could create a
magnetic field. And he was right....
4
A traveling electromagnetic disturbance
Assuming Maxwell was right, an amazing thing can happen:
if you can somehow produce a varying electric field,
then that will create a varying magnetic field,
which will continue to create a varying electric field,
which will continue to create a varying magnetic field,
etc.
Moreover, the fields will move in space as they continue to “bootstrap” one
another. By measuring the strengths of the electric and magnetic forces,
d
q1
q2
Fe = k
q1q2
d2
constant that reflects how
strong the electric force is
Fm = h
I1 I 2
l
d
l
d
constant that reflects how
strong the magnetic force is
I1
I2
Maxwell’s theory predicts the speed of this electromagnetic disturbance:
c= 2
k
≈ 300,000,000 m/s
h
“SI” units of measure
(the metric system)
•
•
•
•
Length: meters (m)
Time: seconds (s)
Velocity: meters/second (m/s)
Frequency: cycles per second or Hertz (Hz)
Hz has units 1/s (“per second” or “inverse
seconds”)
Always state the units for your answers!
Useful conversion: 1 m/s is about 2 mph.
Maxwell’s traveling electromagnetic disturbance has a speed of
about 300,000,000 m/s or 600,000,000 mph -- it’s much easier to
write 3x108 m/s or 6x108 mph.
5
Scientific notation – powers of 10
0.1 = 10-1
1 = 100
10 = 101
1,000 = 1.0 x 103
2,100,000 = 2.1 x 106
1/(1,000) = 0.001 = 10-3
Calculator notation: 2.1 x 106 = 2.1E6
Scientific notation – prefixes
m
μ
n
milli = 10-3
micro = 10-6
nano = 10-9
k
M
G
T
kilo = 103
mega = 106
giga = 109
Tera = 1012
Common usage:
wavelength in mm, μm, or nm
frequency in kHz, MHz, GHz, or THz
6
Self-test you can do at home
Express the following in scientific notation:
1. 137 = ?
2. 299792458 = ?
3. 0.025 = ?
If you learn to do these
quickly, it will save you
time later.
Express the following amounts in different units:
1. 2.5 m = ? km
2. 2450 MHz = ? GHz
3. 1.5x1014 Hz = ? THz
4. 400 nm = ? mm
5. 299792458 m/s = ? m/ns
It doesn’t take much
practice to learn to do
these quickly and
accurately.
Tip for surefire units conversion: multiply by 1, cancel units above and below fraction
E.g.,
3
3.0 ×10 8 m/s = 3.0 ×10 8
=1
1000 m 10 MHz
=
=L
1 km
1 GHz
=1
1=
m ⎛ 3.048 ft ⎞⎛ 1 s ⎞
−1
⎜
⎟⎜
⎟ = 9.1×10 ft/ns ≈ 1 ft/ns
s ⎝ 1 m ⎠⎝10 9 ns ⎠
What is a wave?
A wave is a propagating disturbance;
each “disturbance” disturbs something next to it, which disturbs something
next to it, and so the disturbance travels;
although the things of which the disturbance is made may not travel much
themselves, the wave travels, and it can carry (transport) energy and
momentum.
Water waves, sound waves, and string waves (a violin string) are familiar
examples of waves, though one must observe carefully to distinguish
important wave behaviors.
Heavy traffic can exhibit wave behavior; so can crowds in a stadium. Are
there other examples?
7
The Speed of Light
How fast does light travel?
• Galileo tried to measure the speed of light directly, found out only that light travels
really really fast (1600s)
• Roemer measured the speed of light by observing the moons of Jupiter in different
seasons (1600s)
• Fizeau measured how long it took light to travel to a distant hilltop and back (1800s)
Light travels at about c=3x108 m/s.
But that’s exactly how fast electromagnetic waves travel! (Hertz figured this out, 1888)
Light is an electromagnetic wave, a traveling/propagating disturbance.
side view
end view
8