Ch.24 Gauss's Law In last chapter, to calculate electric filed E at a give location: qi ^ For point charges: Ke 2r i r dq ^ Ke 2 r For continuous charge distributions: r However, for many situations with symmetric charge distribution, Gauss's Law provides

PRL 113, 073003 (2014)
week ending
15 AUGUST 2014
PHYSICAL REVIEW LETTERS
Backaction-Driven Transport of Bloch Oscillating Atoms in Ring Cavities
1
2
J. Goldwin,1 B. Prasanna Venkatesh,2,3 and D. H. J. ODell2
Midlands Ultracold Atom Research Centre, Schoo

Testing the Infinitely Many Genes Model for the Evolution of
the Bacterial Core Genome and Pangenome
R. Eric Collins* and Paul G. Higgs
Origins Institute and Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada
*Correspondin

Testing the Infinitely Many Genes Model for the Evolution of
the Bacterial Core Genome and Pangenome
R. Eric Collins* and Paul G. Higgs
Origins Institute and Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada
*Correspondin

16. Holography
Dennis Gabor (1947) Nobel Prize in Physics (1971)
Photography
Records intensity distribution of light .
+
+
Does not record direction.
Two-dimensional image.
Holography = whole + writing
Records intensity & direction of light.
+
+
+
Infor

26. Nonlinear optics and light modulation
Linear Optics and Nonlinear Optics
Linear Optics
p
z The optical properties, such as the refractive index and the absorption
coefficient are independent of light intensity.
z The principle of superposition holds
h

Chapter 12. Diffraction Grating
Last Lecture
Fraunhofer versus Fresnel Diffraction
Diffraction from a Single Slit
Beam Spreading
Rectangular and Circular Apertures
Resolution
This Lecture
The Grating Equation and Free Spectral Range
Grating Dispers

15. Production of Polarized Light
Last Lecture
Polarized Light
Jones Vectors for Polarized Light
Jones Matrices for Polarizers, Phase Retarders,
Rotators
This Lecture
Dichroic Materials
Polarization by Scattering
Polarization by Reflection from Diel

22.
22. Theory
Theory of
of Multilayer
Multilayer Films
Films
r
Transfer Matrix
Reflectance at Normal Incidence
Anti-reflecting Films
High-Reflectance Films
Ea
B M1 M 2 M 3 .MN
a
EN
EN
M
T
B
B
N
N
m11
m
21
m12
m22
EN
B
N
t
Transfer
Tra

23. Fresnel Equations
EM Waves at boundaries
Fresnel Equations:
Reflection and Transmission Coefficients
Brewsters Angle
Total Internal Reflection (TIR)
Evanescent Waves
The Complex Refractive Index
Reflection from Metals
We will derive the Fresnel

LAST (Family) NAME:
-w_
FIRST NAME:
ID # : '
MATHEMATICS 3DC3
McMaster University Final Examination Dr. D. Pelinovsky
Day Class '
Duration of Examination: 3 hours December 8, 2010
THIS EXAMINATION PAPER INCLUDES 16 PAGES AND 5 QUESTIONS. YOU
ARE RESPONSIB

20.
20. Aberration
Aberration Theory
Theory
Wavefront aberrations ()
Chromatic Aberration ()
Third-order (Seidel) aberration theory
Spherical aberrations
Coma
Astigmatism
Curvature of Field
Distortion
Aberrations
Aberrations
Chromatic
n ( )
Monoch

19.
19. Optics
Optics of
of the
the eye
eye
Human
Human Eye,
Eye, Relaxed
Relaxed
20 mm
15 mm
n = 1.45
n = 1.33
F
H H
F
P = n/f2 = 1.334/20mm = 66.7 Diopter (1/m)
3.6 mm
7.2 mm
Accommodation
Accommodation (
( )
)
Refers to changes undergone by lens to en

14.
14. Matrix
Matrix treatment
treatment of
of polarization
polarization
This lecture
Polarized Light : linear, circular, elliptical
Jones Vectors for Polarized Light
Jones Matrices for Polarizers, Phase Retarders, Rotators
x
(Linear) Polarization
z
y

LAST NAME:
FIRST NAME:
ID # :
MATHEMATICS 3Q03
McMaster University Final Examination Dr. D. Pelinovsky
Day Class
Duration of Examination: 3 hours , 7 _ ' April 26, 2013
THIS PAPER INCLUDES 16 PAGES AND 5 QUESTIONS. YOU ARE RE-
SPONSIBLE FOR ENSURING THAT

Lecture Notes on PDEs:
Separation of Variables and Orthogonality
Richard H. Rand
Dept. Theoretical & Applied Mechanics
Cornell University
Ithaca NY 14853
[email protected]
http:/audiophile.tam.cornell.edu/randdocs/
version 15
Copyright 2008 by Richard H. R

Determination of Plancks Constant Using the Photoelectric Effect
Lulu Liu (Partner: Pablo Solis)
MIT Undergraduate
(Dated: September 25, 2007)
Together with my partner, Pablo Solis, we demonstrate the particle-like nature of light as characterized by phot

Mathematica for spherical harmonics
Spherical harmonics are built in functions.
Arguments are l, m, ,
Here, for example, are the l=4 harmonics for m=0-4
Table[SphericalHarmonicY[4, m, , ], cfw_m, 0, 4] / TableForm
3 (3-30 Cos[]2 +35 Cos[]4 )
16
- 38
5
3

23.3 Coulomb's Law Like charges
F 12
Examples: r q1 r q2
F 21
q1
Unlike charges q1
F 12
r q2
F 21
q2
q3
The electric force exerted on q2 due to a charge q1:
F 21 = ke
q1q2 ^ r r2
(1785, Charles Coulomb)
For magnitude: |F21| = ke|q1|q2| / r2 q1, q2: charge

Chapter 25 Electric Potential 25.1 Potential Difference and Electric Potential Conservative Forces
Define Electric potential: V= U/q0. V is the potential energy per unit charge. V is a scalar. The potential difference:
V=
U = q0
B E ds A
Gravitational For

Chapter 28 Direct Current circuits 28.1 Electromotive Force (emf) Sources of emf: A battery or any other device that provides electrical energy. "charge pump" r: internal resistance Resistor + _
Example: A battery has an emf of 12 V, and internal resistan

Ch 26. Capacitance and Dielectrics Capacitor: two conductors having equal and opposite charge and a potential difference between them. Use: Commonly used in electronic circuits (tune frequency circuits, AC filter, energy storing)
26.2 Calculation of Capac

Chapter 27 Current and Resistance 27.1 Electric Current Electric current:
dQ 1C , unit: ampere 1A = dt s The rate at which charge flows through a surface. I
No longer have static equilibrium. E and Q can 0 inside a conductor! The direction of the current

Chapter 29 Magnetic Fields Each magnet has two poles, north pole and south pole, regardless the size and shape of the magnet. Like poles repel each other, unlike poles attract each other. Compass: north pole points to the north of the Earth. Magnetic pole

Chapter 31. Fraraday's Law 31.1 Faraday's Law of Induction An induced electric current (or induced emf) could be induced in a circuit by a changing magnetic field. Faraday's Law of induction: The emf induced in a circuit is directly proportional to the ti

Example: A single-turn circular loop of Radius R is coaxial with a solenoid (r = 0.03m, l = 0.75m, 1500 turns). The current decreases linearly from 7.2A to 2.4 A in 0.3 seconds. Calculate the induced emf. Solution: The magnetic field inside the solenoid:

Chapter 32 Inductance Ch. 32.1 Self-Inductance As the resistance changes, the current does not change immediately to its final value I = /R. As the current increases or decreases with time, the magnetic flux through the coil due to its current also change

Chapter 37 Interference of Light Waves 37.1 Conditions for Interference Interference of light waves occurs whenever two or more waves overlap at a given point. Constructive interference: the amplitude of the resultant wave is greater than that of any indi