Download electricity/magnetism

PHYS 1212
Electricity, Magnetism, and Optics
 Prerequisites: PHYS 1211 or 1111, MATH 2200
(calculus)*** also familiarity with college Algebra,
Geometry, Trigonometry**, and Basic Chemistry (Useful
to have MATH 2210 as prereq.)
 Not available for students with credit in PHYS 1112
 Introduction to Optics, Electricity, and Magnetism using
calculus
Aims of course:
- teach you the fundamental principles/laws of physics
- teach you how to apply these principles to practical
problem solving (useful in other fields)
A Building-Up of Principles
Algebra -> geometry -> trigonometry-> kinematics ->
forces -> work/energy -> … -> oscillations/waves -> …
-> optics -> electricity/magnetism -> special
relativity -> quantum mechanics -> ….
Why Optics, Electricity, Magnetism?
Physics could be defined as the study of energy and
matter. Light is a form of energy and is a manifestation of
electro-magnetic forces.
In PHYS 1211 (or 1111), we mostly considered the force
of gravity or indirect manifestations of the electro-magnetic
force (friction, normal force).
In this course, we will study the fundamental forces of
electricity and magnetism.
The Classification of Physics
Classical Physics
- everyday speeds and sizes
(Newton, Maxwell,…)
Quantum Physics
- very small
(Schroedinger, …)
Relativistic Physics
- Very fast (Einstein, …)
Relativistic Quantum
Physics – very small and
very fast (Dirac, …)
Introduction and Review
Things you should already know or will need to learn
about:
1. Units: SI will be used (mostly), British units will be
used rarely (foot, pound…)
2. Significant figures (covered in PHYS 1211 lab)
3. Dimensional analysis
4. Order-of-magnitude estimates
5. Everything from PHYS 1211 up to and including
waves
Review of Wave Properties
The particle-wave duality of light:
- Classical electro-magnetic theory
describes light as a wave (Chap. 34)
- Quantum-mechanically, light is made up
of particles, each with some “quanta” or
packet of energy – photons (Chap. 40)
In this course, we will treat “light” as a wave
Specifically, light is a transverse, periodic
wave
You should review Chap. 16 (sections 1, 2, 4)
Periodic wave

y
A
x

y
T
A
t
T
Can have wave motion in both time (same as simple
harmonic motion) and space (x-direction for example)
  = wavelength, the length of one complete
wave cycle; units of m
 Analogous to the Period T of a wave (for motion
in time). In fact they are related
v
  vT 
f
1
T
f
 Where v is the velocity of the wave. It is the
velocity of a point on the wave (crest, trough, etc).
For light, v=c, the speed of light.
 Since wave motion can be in space and time, we
would like to have an equation for the magnitude
of the wave (y) as a function of space and time
 The magnitude of the wave as a function of t
and x (without proof):
 2 x

y  A sin 
 2 ft   A sin kx  t 
 

(-) positive x-direction wave motion
(+) negative x-direction wave motion
k=2/, the angular wave number
 The quantity in parentheses is dimensionless
(radians) and is called the phase angle () of a
wave
y  A sin   A cos  2 
 The correspondence with Simple Harmonic
Motion should be apparent
What is y for a light wave?
y
The wave
magnitude is the
oscillating electric
and magnetic field
We take the wave
to move at speed c
along the x-axis
f

The electromagnetic
spectrum
(Section 34.6)
Chapter 35. Geometric Optics
What is optics? The study of how light
behaves as it encounters different media
during its propagation through space
Why study optics? We can understand how
many things work: the eye, glasses, cameras,
telescopes, …, the effects at Disney’s
Haunted Mansion, …
Light sources are generally point sources that
emit spherical waves
A wave front is a point on the wave (peak or
trough) that propagates at speed c with the
wave
A ray defines the direction of the wave and is
perpendicular to the wave front
We adopt the ray
approximation which
assumes that the wave
moves through a medium in
a straight line in the
direction of the rays
At a sufficiently far distance
from the source, a spherical
wave can be approximated
as a plane wave
Law of Reflection
Consider light (here a plane wave illustrated
by a number of rays) striking a reflective
surface
If the surface is smooth, the rays will
“bounce” off of the surface in a
“orderly” manner
– specular reflection
If the surface is rough, the rays will reflect in
random directions – diffuse reflection
We will mostly consider
smooth surfaces
It turns out for smooth
surfaces that the angle of
reflection equals the angle of
incidence – the law of
reflection

1  1
Snell’s Law of Refraction
Consider “light” propagating in one “transparent”
medium (e.g. air). It encounters a boundary to
another “transparent” medium.
Some of the light is reflected,
while some of the light travels
into the second medium
Note, we will not worry here
about the intensities of the
incident, reflection, and
transmitted beams
When light travels through any medium, its
speed v < c, since c is the speed of light in a
vacuum. However, the speed of light in air is
 c=v1.
After the light enters the new medium (e.g.
glass), its speed v2 decreases
Since the speed changes,
the ray is bent and
propagates through the
second medium at a new
angle:
sin  2 v 2

 constant
sin 1 v1
What is this constant? It is related to the two
media that the light propagates through.
For any medium, we can make the following
definition from the ratio:
(speed of light in vacuum)/(speed of light in
the medium)
or
c
n
v
n is the index of refraction. n  1. Table 35.1
gives the index of refraction for some materials.
Examples: air (1.0003), glass (1.52), diamond
(2.42).
Therefore, using the index of refraction in the
previous relation gives
sin  2 v 2 c/n2


sin 1 v1 c/n1
or
n1 sin 1  n2 sin  2
which is Snell’s law of refraction.
c
f

Note that
n2 


v2
f 2 2 2
since the frequency does not change.