Physics 422 - Spring 2013 - Assignment #6, Due April 14th
1. (Hecht, 8.16) Two ideal linear sheet polarizers are arranged with respect
to the vertical with their transmission axis at 10 and 60 , respectively. If a
linearly polarized beam of light with its
Physics 42200
Waves & Oscillations
Lecture 28 Geometric Optics
Spring 2014 Semester
Matthew Jones
Thick Lens: equations
Note: in air (n=1)
1 1 1 xo xi = f 2
+=
so si f
effective
focal length:
Principal planes:
1
1
1 (nl 1)d l
= (nl 1)
+
f
R1 R2
nl R1R2
Physics 42200
Waves & Oscillations
Lecture 27 Geometric Optics
Spring 2014 Semester
Matthew Jones
Thin Lens Equation
First surface:
Second surface:
Add these equations and simplify using
11
1
1
1
(Thin lens equation)
1 and
0:
Thick Lenses
Eliminate the
Physics 42200
Waves & Oscillations
Lecture 25 Propagation of Light
Spring 2014 Semester
Matthew Jones
Geometric Optics
Typical problems in geometric optics:
Given an optical system, what are the properties
of the image that is formed (if any)?
What con
Physics 42200
Waves & Oscillations
Lecture 26 Geometric Optics
Spring 2014 Semester
Matthew Jones
Sign Conventions
+
=
>
Convex surface:
is positive for objects on the incident-light side
is positive for images on the refracted-light side
is positive if
Physics 42200
Waves & Oscillations
Lecture 24 Propagation of Light
Spring 2014 Semester
Matthew Jones
Midterm Grades
Spring 2014 midterm
(out of 40)
Mean is 53.5 1.3%
Spring 2013 midterm
(out of 60)
Mean is 47.1 1.3%
Geometric Optics
Wave equation in fre
Physics 42200
Waves & Oscillations
Lecture 22 French, Chapter 8
Spring 2014 Semester
Matthew Jones
Midterm Exam:
Date:
Time:
Room:
Material:
Thursday, March 13th
8:00 10:00 pm
PHYS 112?
French, chapters 1-8
Waves in Three Dimensions
The excess pressure i
In[1]:=
For a string of length L, tension T and mass per unit length ,
the wave velocity is given by
T
v:
and the frequency of the normal modes of oscillation are
In[2]:=
n
T
L
n_
:
In[3]:=
a general solution to the wave equation with boundary conditions
For a string of length L, tension T and mass per unit length ,
the wave velocity is given by
T
v:
and the frequency of the normal modes of oscillation are
n
T
L
n_
:
a general solution to the wave equation with boundary conditions y 0
yL
0 can be written
Physics 42200
Waves & Oscillations
Lecture 31 Polarization of Light
Spring 2014 Semester
Matthew Jones
Types of Polarization
Light propagating through different materials:
One polarization component can be absorbed
more than the other
One polarization
Physics 42200
Waves & Oscillations
Lecture 32 Polarization of Light
Spring 2014 Semester
Matthew Jones
Polarization
( , )=
cos
( , )=
cos
+
Unpolarized light: Random
,
,
Linear polarization: = 0,
Circular polarization:
=
and
=
Elliptical polarizati
Physics 42200
Waves & Oscillations
Lecture 30 Electromagnetic Waves
Spring 2014 Semester
Matthew Jones
Electromagnetism
Geometric optics overlooks the wave nature of
light.
Light inconsistent with longitudinal waves in an
ethereal medium
Still an excel
Physics 422 - Spring 2014 - Assignment #4, Due March 10th
1. A string of length L = 8 m, tension T = 4 N and linear mass density
= 1 kg/m is initially at rest, but has an initial displacement described by
the function
0
f (x) = 1
0
11
00
11
00
11
00
11
0
Physics 422 - Spring 2013 - Assignment #5, Due April 4th
1. (Hecht, 5.22) Determine the focal length in air of a thin spherical planarconvex lens having a radius of curvature of 50.0 mm and an index of refraction
of 1.50. What, if anything, would happen t
Physics 422 - Spring 2014 - Assignment #3, Due February 28th
1. A log with mass M = 100 kg is oating in Lake Michigan, which contains
fresh water, so its density is = 1 g/cm3 . The log has a cross sectional area,
A = 500 cm2 , and is oriented vertically a
Physics 422 - Spring 2014 - Assignment #2, Due February 7th
1. A mass attached to a spring (which has neglibible mass) is described by
the dierential equation
mx + bx + kx = 0
(1)
which has a solution that can be written
x(t) = Aet/2 cos(t).
(2)
What is t
Physics 422 - Spring 2013 - Assignment #1, Due January 24th
1. Show that the complex valued function
z (t) = aei eit + bei eit
can be written in the form
z (t) = rei(t+)
and nd expressions for r and in terms of the real numbers a, b, and .
2. A mass is sl
Physics 42200
Waves & Oscillations
Lecture 29 Geometric Optics
Spring 2014 Semester
Matthew Jones
Aberrations
We have continued to make approximations:
Paraxial rays
Spherical lenses
Index of refraction independent of wavelength
How do these approxim
For a string of length L, tension T and mass per unit length ,
the wave velocity is given by
T
v:
and the frequency of the normal modes of oscillation are
n
T
L
n_
:
a general solution to the wave equation with boundary conditions y 0
yL
0 can be written
Physics 42200
Waves & Oscillations
Lecture 18 French, Chapter 6
Spring 2014 Semester
Matthew Jones
Wave Equation
=
1
Speed of propagation depends on the medium:
String with tension
and linear mass density :
= /
=
/
Electrical transmission lines:
Soun
Physics 42200
Waves & Oscillations
Lecture 17 French, Chapter 6
Spring 2014 Semester
Matthew Jones
Other Continuous Systems
=
Equal and opposite forces squish the cube of elastic
material. Net force is zero so there is no acceleration.
=
Other Continuous
Physics 42200
Waves & Oscillations
Lecture 16 French, Chapter 6
Spring 2014 Semester
Matthew Jones
Continuous Systems
=
In the limit
where
=
=
/.
this becomes the wave equation:
1
=
Other Continuous Systems
1. Longitudinal waves in a solid elastic rod