Physics 422 - Spring 2013 - Assignment #1, Due January 18th
1. Consider the dierential equation
d2 x
+ 2x = 0
dt2
(1)
If a general solution is written in the form of the innite series,
an tn
x(t) =
n=0
what constraints must the coecients an satisfy if x(t
Physics 422 - Spring 2013 - Assignment #8, Due March 29th
1. Brewsters angle corresponds to the angle of incidence for which rk = 0
when light in a medium with index of refraction n1 is incident on the surface
of another medium with index of refraction n2
Physics 422 - Spring 2013 - Assignment #10, Due April 15th
1. (Hecht, 9.12) With regard to Youngs Experiment, derive a general expression for the shift in the vertical position of the mth maximum as a result
of placing a think parallel sheet of glass of i
Physics 422 - Spring 2013 - Assignment #7, Due March 1st
1. The radial wave equation in two dimensions is written:
2 1 2
+
+ 2 = 0.
r2
r r
v
Rotationally symmetric solutions to the wave equation in two dimensions
which are finite at r = 0 are the Bessel
Physics 422 - Spring 2013 - Assignment #2, Due January 25th
1. (French 3-10) A metal rod, 0.5 m long, has a rectangular cross section of
area 2 mm2 .
(a) With the rod vertical and a mass of 60 kg hung from the bottom, there is
an extension of 0.25 mm. Wha
Physics 422 - Spring 2013 - Assignment #9, Due April 8th
1. (Hecht, 5.30) Write an expression for the focal length (fw ) of a thin lens
immersed in water (nw = 4/3) in terms of its focal length when in air (fa ).
2. (Hecht, 5.25) A candle that is 6.00 cm
Physics 422 - Spring 2013 - Assignment #6, Due February 22st
1. (French, 6-14) Find the Fourier series for the following functions
(0 x L):
(a)
(b)
(c)
2.
length
(a)
(b)
y(x) = Ax(L x)
y(x) = (
A sin(x/L)
A sin(2x/L)
y(x) =
0
0 x L/2
L/2 x L
(French 6-15)
Physics 422 - Spring 2013 - Assignment #11, Due April 22th
1. (Hecht, 10.1) Consider the diagram below, in which a light source S is
located a perpendicular distance R from a circular aperture of radius a. The
conditions for Fraunhofer diffraction are tha
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Physics 422 - Spring 2013 - Midterm Exam, March 6th
Answer all questions in the exam booklets provided.
There are 6 questions - please answer all of them.
Explain your reasoning clearly but concisely.
Clearly indicate which work is to be graded.
Each ques
Physics 422 - Spring 2013 - Midterm Exam, March 6th
Answer all questions in the exam booklets provided.
There are 6 questions - please answer all of them.
Explain your reasoning clearly but concisely.
Clearly indicate which work is to be graded.
Each ques
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Physics 422 - Spring 2013 - Assignment #3, Due February 1st
1. (French, 4-4) A block of mass m is connected to a spring, the other end
of which is fixed. There is also a viscous damping mechanism. The following
observations have been made on this system:
Physics 422 - Spring 2013 - Assignment #4, Due February 8st
1. (French, 5-9) The CO2 molecule can be likened to a system made up of
a central mass m2 connected by equal springs of spring constant k to two
masses m1 and m2 (with m1 = m2 ) as shown:
O
16
C
Physics 422 - Spring 2013 - Assignment #5, Due February 15st
1. (French, 6-2) A string of length L and total mass M is stretched to
a tension T . What are the frequencies of the three lowest normal modes of
oscillation of the string for transverse oscilla
Chapter Chapter 2 Wave Motion III Motion III
3-D Waves: Plane Waves
(simplest 3-D waves) All the surfaces of constant phase of the disturbance form parallel planes that are generally perpendicular to the propagation direction An equation of a plane that i
Electromagnetic Theory, Electromagnetic Theory, Photons, and Light I
Classical EM Waves versus Photons
The energy of a single light photon is E=h energy of single light photon is
c The Plancks constant h = 6.62610-34 Js E1 = h = h 4 1019 J Visible light w
Electromagnetic Theory Electromagnetic Theory, Photons and Light II Photons, and Light II
Maxwells Equations
Gausss Gausss Faradays AmpreMaxwells
B dS = 0
S
E dS = q
S 0
1
In vacuum (free space) space)
d CE dl = dt
[ B dS ]
A
E CB dl = 0 A J + 0 t dS
Electromagnetic Theory Electromagnetic Theory, Photons and Light III Photons, and Light III
The Poynting Vector: Polarized Harmonic Wave
E = E0 cos k r t
0
[ ] B = B cos[k r t ]
( )
Polarized EM wave:
S=
1
0
EB
Poynting vector: 1 S= E0 B0 cos 2 k r t 0
[
The Superposition of Waves The Superposition of Waves I
Principle of Superposition
Wave equation:
1 2 2 2 2 + 2+ 2= 2 2 2 z x y v t
(r , t ) = Ci i (r , t )
i =1
n
If i are solutions of the wave equation, then their linear solutions of the wave equation