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PHY 228: Optics, Relativity, and Thermal Physics
Professor: Joseph Brill, CP381, 7-4670, [email protected]
Class Time: MWF 12, CP222
Office Hours: W, R 10:30-11:30
Course Website: http://www.pa.uky.edu/~brill/PHY228/
Required Text: Physics For Scientists and Engineers (9th Ed.)
Serway and Jewett (Cengage Learning)
[webassign and/or hybrid copy and/or hardcopy (8th or 9th)]
[The webassign website is: https://webassign.net/ ]
.
Optics: The Study of Light
Light: an Electromagnetic Wave
(propagating oscillations of electric (E) and magnetic (B) fields)
But what are Electric and Magnetic Fields?
Consider the gravitational field
(g, ). It points in the
direction of the acceleration
due to gravity of any mass (m)
at that point, and the strength
of the field (length of arrow) is
proportional to the magnitude
of the acceleration. Near a
mass M,

agrav = g = -GM r /r2.
Since Fgrav = magrav = mg
g = Fgrav /m .
earth
Near the earth, g points
toward the center of
the earth. Near the
surface, it is
approximately vertically
down with
approximately constant
magnitude 9.8 m/s2.
Similarly, an electric field
(E) surrounds an electric
charge (q), with the field
pointing away from a
positive charge and toward
a negative charge. If
another charge (Q) is
placed in the field, it will
feel a force in the direction
of E if Q is positive and
opposite E if Q is negative:
F = QE
Note that this implies that
like-sign charges repel and
opposite-sign charges
attract.
If more than one
charge is present,
add the (vector)
electric fields of
each. Two examples:
A magnetic field (B
)
surrounds a bar magnet, and
points in the direction that a
compass needle at each position
would point. It can also be
mapped by sprinkling iron
powder around the magnet.
More complicated patterns:
The magnetic field is created by spinning electrons (which are “nanoscopic” electric
currents) in the bar magnet and interacts with the compass needle or iron filings
through their own spinning electrons (“nanoscopic” currents).
More fundamentally, a magnetic field
surrounds any moving charge (e.g. an
electric current) and interacts with any
other moving charge (or current):
FB = Q v x B
Therefore, the total electric and magnetic
force on a charge is:
F = QE + Q v x B
Electric fields (E) surround electrical charges and magnetic fields (B)
are created by moving (or spinning) charges (currents).
Faraday showed that electric fields can also be created by changing
magnetic fields and Maxwell showed that magnetic fields could also
be created by changing electric fields. These effects are summarized
in “Maxwell’s Equations.” (Eqtns. 34.4-34.7, to be studies in PHY232)
Consider a material in which there are no free charges or currents and
in which the electric field points in the y-direction but is changing
along the x-direction. Then if Ey changes in time, it creates a Bz , and
Maxwell’s Eqtns. reduce to:
Ey/x = - Bz/t
(1)
Ey/t = - ()-1 Bz/x (2)
(Note that Ey and Bz are both functions of x and t.)
 and  are the dielectric constant and magnetic susceptibility of the
material, which are measures of how much bound charges and spins
in the material can respond to electric and magnetic fields.
dielectric material
Ey/x = - Bz/t
(1)
Ey/t = - ()-1 Bz/x (2)
can change order of
differentiation
Differentiate Eqtn. (1) with respect to x:
2Ey/x2 = - (Bz/t)/x = - (Bz/x)/t = 2Ey/t2
or
2Ey/t2 = ()-12Ey/x2
(3)
This is just the wave equation (Eqtn. 16.27: 2y/t2 = v22y/x2 ),
where
 = 1 /v2, the speed of the wave.
The solutions are traveling waves of the form (Eqtn. 16.5):
Ey = Ey0 sin [2π(x  vt)/], Bz = Bz0 sin [2π(x  vt)/],
- sign: wave traveling toward positive x.
+ sign: wave traveling toward negative x

v
Ey = Ey0 sin [2π(x  vt)/], Bz = Bz0 sin [2π(x  vt)/],
Ey/x = - Bz/t
Bz/t = (2πv/ ) Bz0 cos[2π(x  vt)/],
Ey/x = (2π/ ) Ey0 cos [2π(x  vt)/],
 Bz0 = Ey0/v.
(The + sign is for a wave traveling toward -x and the minus sign is for a wave
traveling toward +x.)
 is the wavelength of the wave and its frequency is f = v/.

v
Problem: An electromagnetic wave has wavelength = 700 nm = 7 x 10-7 m and speed
3 x 108 m/s. The magnitude of its electric field is E0 = 600 V/m (low power laser)
a) What is the frequency of the wave?
b) What is the magnitude of its magnetic field?
Problem: An electromagnetic wave has wavelength  = 700 nm = 7 x 10-7 m and speed
v = 3 x 108 m/s. The magnitude of its electric field is E0 = 600 V/m (low power laser).
a) What is the frequency of the wave?
b) What is the magnitude of its magnetic field?
a) f = v/ = (3 x 108 m/s) / ( 7 x 10-7 m) = 4.3 x 10 14 /s = 4.3 x 1014 Hz (Red light)
b) B0 = E0/v = (600 V/m) / (3 x 108 m/s) = 2 x 10-6 Vs/m2 = 2 x 10-6 Tesla (~ 4% of earth/s B-field)