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Transcript
Physics 24100
Electricity & Optics
Lecture 28 – Review of chapters 29-33
(Lectures 19-27)
Fall 2012 Semester
Matthew Jones
ANNOUNCEMENT
*Exam 1: Friday December 14, 2012, 8 AM – 10 AM
*Location: Elliot Hall of Music
*Covers all readings, lectures, homework from Chapters 29
through 33.
*The exam will be multiple choice.
Be sure to bring your student ID card and a handwritten one-page (two sided) crib sheet plus the crib
sheets that you prepared for exams 1 and 2.
NOTE THAT FEW EQUATIONS WILL BE GIVEN – YOU ARE REMINDED THAT IT IS YOUR
RESPONSIBILITY TO CREATE WHATEVER TWO-SIDED CRIB SHEET YOU WANT TO BRING
TO THIS EXAM.
The equation sheet that will be given with the exam is posted
on the course homepage. Click on the link on the left labeled
“EquationSheet”
Review of Chapters 29-33
This lecture reviews some, but not all
of the material that will be on the final
exam covering Chapters 29-33.
Alternating Current Circuits
Stored energy:
1
=
2
1
=
2
1
=
2
Oscillation frequency:
1
=
RLC Circuit:
=
=
/
cos
"
−
2
+
−
+!
( )
( )
#
Time Varying EMF
Relation between
and
ℇ
= ℇ sin
ℇ
= sin
"
Voltage and current are in phase.
(
ℇ
=
sin
)(
)( = 1⁄
+ 90°
“Voltage lags the current by 90 degrees”
ℇ
= sin
)
“Voltage leads the current by 90 degrees” ) =
− 90°
Phasor Diagrams
Transformers
Primary winding:
./ turns.
Applied EMF:
0Φ
/ = −./
0
Secondary winding:
.2 turns.
Induced EMF:
0Φ
2 = −.2
0
Equal flux Φ through
both windings.
/
./
=
Secondary EMF:
2
.2
2
=
34
/3
5
Step-up transformer: .2 ⁄./ > 1 and
Step-down transformer: .2 ⁄./ < 1 and
2
2
>
<
/
/
RMS Voltage and Current
8 9:
<9= =
;2
(for sinusoidal waveforms)
=
1
2
8 9:
=
"
;2
8 9:
"
=
8 9:
2
Maxwell’s Equations
FG?HGDI
@ ∙ B DE = > ?
JK
C
@ ∙ L DE = K
> ?
C
DNO
> B ∙ Dℓ = −
D
> L ∙ Dℓ = PK
Gauss’s Law
“No magnetic monopoles”
Faraday’s Law
DNI
+ PK QK
D
Ampere’s Law with
displacement current
Maxwell’s Equations in Free Space
DNO
> B ∙ Dℓ = −
D
DNI
> L ∙ Dℓ = PK QK
D
VW X,
R S BT
R S BT
= PK JK
S
RU
R S
= V sin ZX −
= 2[\ = Z] = 2[]/^
1
]=
= λ\
_ `
Characteristics
• V and b are perpendicular
then b = b sin ZX −
• If V = V sin ZX −
e×g
d
• The Poynting vector, c =
is in the direction of
propagation
hi
• V and b are perpendicular to cd
x
z
1/2/2013
S
12
Energy of Electromagnetic Waves
• Energy stored in electromagnetic waves:
n
=
1
n = ` V
2
o
b
hi
n
o
b = V ⁄] = V _ `
= ` V =n
• Light intensity:
=
– Power per unit area
ej
hi k
• Radiation pressure: <l =
– Force per unit area
1
=
b
2_
m
k
Polarized Light
Polarizers transmit only the component
of V parallel to the polarizing axis.
If the incident light is un-polarized, the
intensity is reduced by 1/2.
Two polarizers:
Malus’s Law:
=
cos p
Geometric Optics
poq
po
p
ro
r
Reflection:
q
po = po
Refraction:
ro sin po = r sin p
(Snell’s law)
In a material with index of refraction, r > 1:
k
• Speed of light: s =
t
• Wavelength: ^q = ^/r
Total Internal Reflection
Critical angle p( defined by r sin p( = 1.
At angles greater than p( , all light is
reflected from the surface.
Chromatic Dispersion
• The index of refraction depends on
the wavelength of light
– It is usually larger at shorter
wavelengths.
Optical Images from Mirrors
For spherical mirrors,
u
\=
2
1 1 1
+ =
v v′ \
v′
x=−
v
Concave mirrors:
u > 0 and \ > 0
Convex mirrors:
u < 0 and \ < 0
Refraction from one Surface
• Snell’s Law:
ro sin po = r sin p
y
ro
v
v′
r > ro
ro po = r p
ro r
r − ro
+
=
v
v′
u
If the surface is concave, then u < 0
Optical Images from Lenses
o
z
• Lens-maker’s formula: = (r − 1)
•
•
o
o
o
Thin lens equation: + =
|}
|~
z
•~
|~
Magnification: x = = −
•}
|}
o
{
−
o
j
Optical Images from Lenses
• Concave lenses have \ < 0
o
z
• Lens-maker’s formula: = (r − 1)
•
•
o
o
o
Thin lens equation: + =
|}
|~
z
•~
|~
Magnification: x = = −
•}
|}
o
{
−
o
j
Systems of Lenses
1
1
1
+
=
0€,o 0•,o \o
ℎ•,o
x = xo x =
ℎ€,o
1
1
1
+
=
0€,
0•,
\
ℎ•,
ℎ€,
ℎ•,
=
ℎ€,o
Interference and Diffraction
Huygens’ principle:
• Each point on a
propagating wave-front
acts like a source of
spherical waves
• These interfere
destructively except in the
forward region or when
obscured by an obstacle.
Interference
• Destructive interference:
…
– Path length differs by Δ„ = x where x = 0,1,2,
• Constructive interference:
– Path length differs by Δ„ = x^
• Phase differences caused by
– Different path lengths
– Different indices of refraction
– Reflection from a surface with larger r
Interference
tan p = ˆ/
Constructive interference:
0 sin p = x^
Maximum intensity occurs at
^
ˆ = x
0
Interference from Thin Films
• Light reflected from the top surface has a phase shift of ^/2.
• Wavelength in the film: ^q = ^/r
• Number of wavelengths in distance 2 is 2 ‰
• Bright fringes when 2 = x + 1/2
• Dark fringes when 2 =
…
x t
…
t
…
t
Diffraction
Position of minima for light transmitted through
an single slit of width Š:
^
x = 1,2,3, …
ˆ •t = x
Š
For a circular aperture of diameter •:
^
sin p •t = 1.22
•
Rayleigh’s criteria:
• Images are resolvable when
1.22^
o
Δp > p = sin
•
Diffraction Gratings
δ
d
θ
θ
. lines per unit length.
• Constructive interference when
• = 0 sin p = x^
• Width of individual lines is
^
∆p =
.0
• Resolving power:
^
x^
"=
=
= x.
0‘p
Δ^
Main application:
Determining ^ by measuring p when . is known.
The Very Last Clicker Question
• My favorite part of the course was:
(A)
(B)
(C)
(D)
(E)
Charges, potential, electric fields
Magnetic fields, induction, RLC, etc.
Optics: lens, mirrors, interference, diffraction, etc.
I don’t know and after the final I never want to
think about this material again.
All of the material and I hope to use some or all this
material in my future career.