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Chapter 33b
Course: PHY 2048 PHY, Spring 2009School: University of Florida
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33: Chapter Electromagnetic Waves ! ! ! ! ! ! Electromagnetic waves. HITT question #1. Radiation pressure. Polarization. HITT question #2. Reflection and refraction. November 13, 2009 Ch. 33: Electromagnetic Waves - Part B 1 The Spectrum of EM Waves ! Maxwells rainbow. November 13, 2009 Ch. 33: Electromagnetic Waves - Part B 2 The Traveling Electromagnetic Wave ! Generation of EM waves ( ~ 1m,...
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33: Chapter Electromagnetic Waves
! ! ! ! ! !
Electromagnetic waves. HITT question #1. Radiation pressure. Polarization. HITT question #2. Reflection and refraction.
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
1
The Spectrum of EM Waves
!
Maxwells rainbow.
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
2
The Traveling Electromagnetic Wave
!
Generation of EM waves ( ~ 1m, short-wave radio).
!
!
!
An LC oscillator produces an AC or oscillatory current at an angular frequency of = 1/ LC . An external energy source supplies energy to compensate for the thermal loss and the energy carried away by the radiated EM wave. The LC oscillator is coupled by a transformer and a transmission line to an antenna.
Ch. 33: Electromagnetic Waves - Part B 3
November 13, 2009
The Traveling Electromagnetic Wave
!
For a wave traveling toward point P in the +x direction:
E y = Em sin( kx t )
Bz = Bm sin( kx t )
Em
A snapshot of an EM wave.
! ! ! !
Bm
E = =c B
is the angular frequency, and k is the angular wave number. The speed of a wave is v = / k , where k = 2 / . The speed of the EM wave is c = 1/ = 3.0 108 m/s . 00 All electromagnetic waves have the same speed c in vacuum.
November 13, 2009 Ch. 33: Electromagnetic Waves - Part B 4
Energy Transport
!
The rate of energy transport per unit area is described by the Poynting vector S. ! 1! ! S= E B Unit is W/m2.
! S gives the EM wave direction of the travel.
!
0
The intensity of the EM wave is:
I = Savg =
1 c 0
E
2 rms
1 2 = Em 2 c 0
(isotropic source with power Ps, emitting light at a distance r )
5
I=
power area
=
Ps 4r 2
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
Energy Transport Example
!
Assume that a TV station acts as a point source broadcasting isotropically at 1.0 MW. What is the intensity of the transmitted signal reaching Proxima Centauri (the star nearest our solar system), 4.3 ly away?
1 ly or 1 light-year is the distance light travels in one year.
1 year = 365 days 24 hours 60min 60 s=31536000 s
1 ly = tc = 31536000 s 3.0 108 m / s = 9.46 1015 m
I=
Ps 4r 2
=
1.0 106 4 ( 4.3 9.46 1015 )2
= 4.8 1029 W/m2
6
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
The Traveling Electromagnetic Wave
!
For a wave traveling toward point P in the +x direction:
E y = Em sin( kx t ) Bz = Bm sin( kx t ) !! +y, +z, +x (RHR) E B
!
If an EM wave has:
E y = Em sin( kx + t )
The direction of the travel is -x. ! Bz = Bm sin( kx + t ) or B = kBm sin( kx + t )
!
If an EM wave has:
November 13, 2009
By = Bm sin( 6 z t )
The direction of the travel is -z.
E x = Em sin( 6 z t )
7
Ch. 33: Electromagnetic Waves - Part B
HITT Question
!
If the magnetic component of a polarized wave is given by: Bx = ( 4.00 T ) sin[ ky + ( 2.00 1015 s 1 ) t ] In which direction does the wave travel, and parallel to which axis is the electric field?
(a) +y, z; (b) -y, x; (c) +x, y; (d) -y, z; (e) +y, x.
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
8
HITT Question
Answer: (d) -y, z
Bx = Bm sin( ky + t ) ! B = + iBm sin( ky + t )
The direction of the travel is -y.
! 1! ! S= E B
direction of the travel.
! S gives the EM wave
!!! i j k ! 0 0 1 = j 1 0 0
0
E z = Em sin( ky + t ) ! E = kEm sin( ky + t )
The electric field is (polarized) parallel to the z axis.
November 13, 2009 Ch. 33: Electromagnetic Waves - Part B 9
Radiation Pressure
!
!
!
Electromagnetic waves have linear momentum as well as energy. EM waves can exert pressure, a radiation pressure, on an object, as we shine light on it. If we shine a beam of EM radiation on an object for a time interval t, and assume that the object is free to move, and that the radiation is entirely absorbed (taken up) by the object. During the interval t, the object gains an energy U from the radiation. Maxwell showed that the object also gains momentum p. U p = (total absorption) c
Ch. 33: Electromagnetic Waves - Part B 10
November 13, 2009
Radiation Pressure
!
!
The direction of the momentum change is the direction of the incident beam of light. If instead of being absorbed, the radiation is completely reflected by the object, back along its original path, then:
2 U p = c
F= I= p t =
(total reflection back along path) (Newtons second law, p=mv)
power area
energy/time area
force pressure = area
11
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
Radiation Pressure
U = IAt
The magnitude the of force on the flat area A, that intercepts the radiation perpendicularly, is:
U IAt IA = = = F= t c t c t c
2 IA F= c
!
p
(total absorption)
(total reflection back along path)
The radiation pressure (unit pascals, Pa), is:
(total absorption)
I pr = c
November 13, 2009
2I pr = c
(total reflection)
12
Ch. 33: Electromagnetic Waves - Part B
Polarization of EM Waves
!
The plane containing the E vectors is called the plane of oscillation of the wave. The wave is plane-polarized in the y direction. Randomly polarized or unpolarized EM waves (Sun, el. bulb). The electric field changes direction randomly, while still perpendicular to the direction of wave travel.
13
!
The wave is traveling out of the page.
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
Polarization of EM Waves
y
!
z
We can represent the unpolarized light as a superposition of two polarized waves, whose planes of oscillation are perpendicular to each other.
y
z
!
The light is partially polarized in the horizontal plane.
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
14
Polarization of EM Waves
!
An electric field component parallel to the polarizing direction is passed (transmitted) by a polarizing sheet; a component perpendicular to it is absorbed. The intensity of the emerging polarized light (if the original light is unpolarized) is: 1 (one-half rule) I = I0 2
!
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
15
Polarization of EM Waves
!
If the light reaching the polarized sheet is already polarized, we can resolve E into two components relative to the polarizing direction of the sheet.
E y = E cos
The intensity is proportional to E2.
is the angle b/w the original and final polarizing directions.
!
The intensity of the emerging polarized light (if the original light is polarized) is:
I = I0 cos2
November 13, 2009
(cosine-squared rule)
16
Ch. 33: Electromagnetic Waves - Part B
Polarization of EM Waves
!
!
!
is the angle b/w the original and final polarizing directions.
November 13, 2009
Light is sent through two polarizing sheets, P1 is polarizer, P2 is analyzer. The transmitted intensity is maximum, and equal to the original intensity when the original wave is polarized parallel to the polarizing direction of the sheet. P2 is polarized vertically. If the polarizing direction of P2 is horizontal, none of the light is transmitted. 1 I = I0 cos2 2
Ch. 33: Electromagnetic Waves - Part B 17
HITT Question 2
!
Four pairs of polarizing sheets are shown, face-on. Each pair is mounted in the path of initially unpolarized light. Rank the pairs according to the fraction of the initial intensity that they pass, greatest first. (a) a,b,c,d; (b) a,d,b,c; (c) d,b,c,a; (d) a,b,d,c; (e) a,b=d,c.
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
18
HITT Question 2
(a) a,b,c,d; (b) a,d,b,c; (c) d,b,c,a; (d) a,b,d,c; (e) a,b=d,c.
0o
60o
90o
30o
I cos2 0 cos2 60 cos2 90 cos2 30 2 2 2 2 I0 I I0
I 1 = cos2 I0 2
1 2
1/ 4 2
0 2
3/4 2
19
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
Reflection and Refraction
!
i 1 1 r
2 normal
The reflected ray lies in the plane of incidence, and the angle of reflection is equal to the angle of incidence.
r
n1 n2
'1 = 1
!
The refracted ray lies in the plane of incidence and has an angle of refraction that is given by Snells law:
n2 sin 2 = n1 sin1
!
All angles are measured with respect to the normal to the interface.
Ch. 33: Electromagnetic Waves - Part B 20
November 13, 2009
Reflection and Refraction
!
!
The index of refraction is a dimensionless constant, depends on the medium/material. Apply Snells law to each interface that the ray (EM wave) reaches.
! ! !
If n2 = n1, 2 = 1. If n2 > n1, 2 < 1. If n2 < n1, 2 > 1.
!
n2 sin 2 = n1 sin1
November 13, 2009
Refraction can not bend a beam so much that the refracted ray is on the same side of the normal as the incident ray.
Ch. 33: Electromagnetic Waves - Part B 21
The Index of Refraction
Some 33-1 TABLEIndexes of Refractiona a Medium Index Vacuum Air (STP)b Water (20 C) Acetone Ethyl alcohol Sugar solution (30%) Fused quartz Sugar solution (80%) 1.00029 1.33 1.36 1.36 1.38 1.46 1.49 Medium Sodium chloride Polystyrene Carbon disulfide Heavy flint glass Sapphire Heaviest flint glass Diamond Index 1.52 1.54 1.55 1.63 1.65 1.77 1.89 2.42 Exactly 1 Typical crown glass
November 13, 2009
Ch. 33: Electromagnetic Waves - Part B
22
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