EXPERIMENT
Electron spin
resonance at DPPH
LOGO
Nguyn Vn ng
L Th Qu
Contents
Theory
Apparatus
Set up and Procedure
Results and discussion
Theory
Electron spin resonance is based on the
absorption of high-frequency radiation by
paramagnetic substances in
1. Prove Snells law by applying Fermats principle. (10%)
Sol.
Pathlength = n1d1 sec 1 + n2 d 2 sec 2 (1)
Pathlength is a function of 1 and 2 , which are related by
d1 tan 1 + d 2 tan 2 = d .(2)
The pathlength is minimized when
( / 1 ) [ n1d1 sec 1 + n2 d
12/05/2007
1. Give three ways for defining the polarization state.
Ans:
(1) the polarization ellipse
(2) the Poincare sphere
(3) the Stokes vector
(4) the Jones vector
2. What is Poincare sphere?
Ans: The Poincare sphere is a geometrical construct in whi
10/03/2007
1. Derive the intensity distribution on a plane for the interference between two oblique plane
waves.
Ans:
U1 = I 0 e j k1 i r = I 0 e jkz
U 2 = I 0 e j k2 i r = I 0 e
j( kx x+ kz z )
= I 0 e j ( k sin x + k cos z )
= 2 1 = k sin x
at z=0 pl
12/12/2007
1. Describe the physical meaning of optical axis for anisotropical
media.
v
Ans: , k (),
na = nb ,(optical axis),
.
2. What is double refraction?
Ans: In anisotropic material, each incident wave has two refracted waves with two
different dire
11/07/2007
1. Interpret the physical meaning of Poynting vector.
Ans: power flow per unit area:
2. Write down the four Maxwell equations in the complete form. Derive the
integral form of four Maxwell equations, and interpret their physical
meanings.
Ans
10/24/2007
1. Prove the Fourier transform of
is
Ans:
s
( t m )
m = s
s
= [ ( t m )]exp ( j 2 t )dt =
m = s
s
m = s
( t m ) exp ( j 2 t )dt
M 1
exp j 2
1 exp ( j 2 M )
2
= exp ( j 2 m ) =
1 exp ( j 2 )
m = s
s
=
(
e j e j M e j M
1 e j 2
)=e
j
I 09/26/2007
1. Why a spherical mirror can not have a rigorous focal point?
Ans:,
,
2. Describe how to use the ray transfer matrix.
Ans: An optical system is a set of optical components placed between two transverse planes at z1 and z2 ,
referred to as t
10/17/2007
1. Define all the parameters which can characterize a Gaussian beam.
Ans: q-parameter z0 (Rayleigh range), Gaussian
beam
q ( z ) = z + jz0
1
1
=
j
, where
q( z ) R( z )
W 2 ( z)
z
Beam width: W ( z ) = W0 1 +
z0
2
z0 2
Wavefront radi
09/19/2007
1. Describe Fermats principle in detail.
Ans:
2. Describe the important characteristics of paraboloidal mirror.
Ans: It has the useful property of focusing all incident rays parallel to its axis to a single point called the
focus.
3. Define pa
Stimulated and Spontaneous Emission of
Radiation in a Single Mode for N-TLMs
Michael T. Tavis and Frederick W. Cummings
The general expressions for the time development of the ensemble averages of and + are found
for N two level molecules (TLMs) interact
Quantum Mechanics
Dung-Hai Lee
Summer 2000
Contents
1 A brief reminder of linear Algebra
1.1 Linear vector space . . . . . . . . . . . . . . . . . . . .
1.2 Linear operators and their corresponding matrices . . .
1.3 Function of an operator . . . . . . .
INSTITUTE OF PHYSICS PUBLISHING
EUROPEAN JOURNAL OF PHYSICS
Eur. J. Phys. 24 (2003) 519524
PII: S0143-0807(03)62660-7
Vector potential of the Coulomb gauge
A M Stewart
Research School of Physical Sciences and Engineering, The Australian National Universit
253a: QFT1
Fall 2008
Matthew Schwartz
Lecture 8:
Gauge invariance
1 Introduction
Up until now, we have dealt with general features of quantum eld theories. For example, we
have seen how to calculate scattering amplitudes starting from a general Lagrangian
Prof. Yen-Chieh Huang
Dept of Electrical Engineering
National Tsing-Hua University
office: EECS516
ext: 4121
email:ychuang@faculty.nthu.edu.tw
EE Photonics I Autumn 2000/01
_
_
Oct. 18, 2000/10/18
EE5140 Photonics I
homework #4
due in class, Tuesday Oct.