Transcript Electromagnetic wave

Light
Physics 202
Professor Vogel
(Professor Carkner’s & CJV notes,
ed)
Lecture 10
Light
Electromagnetic wave
oscillating electric and magnetic fields –
no material medium that is moving!
energy transfer at speed v (c=3X108 m/s in vacuum)
 wavelength = distance between repeats l
 frequency = # repeats per second f
fl=v
v=c in vacuum
c=3X108 m/s
EM Spectrum
The EM Spectrum
 Radio
> 1 meter
penetrates solid objects
easily
 Millimeter (microwave)
1 m - 1 mm
used for communication
 Infrared
1 mm - 700 nm
we feel as heat
 Visible
700-400 nm
eyes evolved to see
 Ultraviolet
400 nm - 100 A
higher energy, causes
sunburn
 X-ray
100 A - 0.01 A
penetrates soft things but
not hard
 Gamma Ray
< 0.01 A
hard to produce and
dangerous
The EM Wave
Lets consider light as a wave
What kind of wave is it?
What is oscillating?
An EM wave consists of an electric field wave
(E) and a magnetic field wave (B) traveling
together
The 2 fields are perpendicular to each other
and to the direction of travel
An EM wave is transverse (like string waves)
The field waves are sinusoidal and in phase
Wave Equations
We can generalize the waves as:
E = Em sin (kx -wt)
B = Bm sin (kx -wt)
Nothing is actually moving
There is no string
A changing E field induces a B field
A changing B field induces an E field
The two fields continuously create each other
The speed of the wave is related to the fields:
c = E/B
Traveling EM Wave
Key Constants
Two important constants in E and M are the
permittivity constant e0 and the permeability
constant m0
Permittivity is the electric force constant:
e0 = 8.85 X 10-12 F/m
In farads per meter
Measure of how electric fields propagate through space
Permeability is the magnetic force constant:
m0 = 1.26 X 10-6 H/m
In henrys per meter
Measure of how magnetic fields propagate through
space
The wave speed depends on these constants:
c = 1/(m0 e0)½
Poynting Vector
EM waves transport energy
The amount of energy delivered per unit area
per unit time is given as flux:
flux = W/m2 = J/s/m2
Flux for an EM wave can be given by the
Poynting vector:
S = (1/m0) EB
However, E and B are related by E/B = c so
we can rewrite S as:
S = (1/c m0) E2
Intensity
The value of S depends on where the
EM wave is in its cycle
We generally are interested in the time
averaged value of S, known as the
intensity
I = (1/c m0) Erms2
Where Erms is the root-mean-square
value of the electric field
Radiation Pressure
EM waves exert a pressure on objects
If someone shines a flashlight on you, the
light is trying to push you away
like ball bouncing off object pushes object back
The force is very small in most cases
EM pressure is due to the fact that light
has momentum which can be
transmitted to an object through
absorption or reflection
Momentum Transfer
The change in momentum due to light is
given by:
Dp = DU/c
Where Dp is the momentum change and DU
is the energy change
The above equation is for absorption
For reflection the momentum change is twice
as much:
Dp = 2DU/c
Light Pressure
From Newton’s second law
F = Dp/Dt
The amount of energy delivered in time Dt is:
DU = I A Dt
where I is the intensity and A is the area
Since pressure (pr) is force per unit area the
pressure becomes:
pr = I/c (total absorption)
pr = 2I /c (total reflection)
Comet HaleBopp
Comet Tails
Light Sail
Color Vision
Rods and cones
one type of cone responds to long l’s: “R”
one type of cone responds to mid wavelengths: “G”
one type of cone responds to short l’s: “B”
How our eyes view pure waves:
red : R-type responds
green : G-type responds
blue : B-type responds
yellow : R- and G-types respond
Cyan: G- and B-types respond
Color Addition
How our eyes view mixtures :
blue + red: R- and B-types respond
 magenta (Like no pure color)
green + blue : G- and B-types respond
 indistinguishable from cyan
red + green : R- and G-types respond
 indistinguishable from yellow
Demo of color addition -- HELP
Color Addition
How our eyes view mixtures :
red + green : R- and G-types respond
 indistinguishable from yellow
red + green + blue : R-, G-, and B-types respond
 white
yellow + blue : R-, G-, and B-types respond
white
Color Subtraction
How our eyes view pigments (absorb
light)
white - blue: R- and G-types respond
 pigment that absorbs blue looks yellow
white - red : G- and B-types respond
 pigment that absorbs red looks cyan
white - (blue + red): G-type responds
 pigment that absorbs blue and red looks green
Color Subtraction
How our eyes view pigments:
white - (blue + red):
 pigment that absorbs blue and red looks green
Pigment: yellow + cyan:
 pigments that absorb blue and red look
green
A demo of subtraction
usflag-neg.gif
Complementary color
= white - color
primary
color
red
green
blue
Complementary
color
cyan
magenta
yellow