Download Review: Self-inductance Review: Electromagnetic Waves Chapter 22

Review: Self-inductance
Announcements
•WebAssign HW Set 8 due this Friday
•Problems cover material from Chapters 22
•Only 3 more HW assignments left
„
Self-inductance: ε = −L
„
RL Circuits:
• The second midterm exam is coming – Monday, Nov 8
•Will cover from 18.1 thru 22.7
•Room assignments TBA
QUESTIONS? PLEASE ASK!
„
Time constant:
„
Current:
I =
„
ε
R
τ =
ΔI
Δt
L=N
ΔΦ B
NΦB
=
ΔI
I
L
R
(1 − e )
−t / τ
Energy stored in an inductor: PEL = ½ L I
2
Review: Electromagnetic Waves
„
Light is an EM wave
„
„
„
„
c=
Speed of light
All EM waves obey c = ƒλ
E and B are transverse
EM waves carry energy:
1
μ oε o
c =
“Bibliotheque Nationale de France”
http://alikaragoz.net/geometric-reflection/
E
B
Average power per unit area =
u⎞
⎛
fo ≈ fs ⎜ 1 ± ⎟
c⎠
⎝
Chapter 22
"Perfect Portage Reflection“
http://www.alaska-in-pictures.com/perfect-portage-reflection-1218-pictures.htm
2
E B
E2
c Bmax
I = max max = max =
2μo
2μo c
2 μo
„
EM waves carry momentum
„
„
„
„
For complete absorption of energy U, p=U/c
For complete reflection of energy U p=(2U)/c
EM spectrum
The Doppler effect for EM waves
Reflection and Refraction
of
Light
u⎞
⎛
fo ≈ fs ⎜1 ± ⎟
c⎠
⎝
1
22.2: Geometric Optics – Using Ray
Approximation
22.1: Dual Nature of Light
„
Light! It’s a wave? It’s a particle? It’s
both!
Some characteristics are explained by wave
nature of light, some are explained better
by particle nature
Experiments display either the wave nature
OR the particle nature of light
„
„
„
„
Very different from other particles; eg, they
have no mass
Light travels in a straight line
in homogeneous media until it
encounters a boundary
between two different media
The ray approximation is used
to represent beams of light
„
„
‘Particles’ of light Æ ‘photons’
„
„
„
„
Rays are perpendicular to
wave fronts
Photon energy E = h ƒ
h = 6.63 x 10-34 J s (Planck’s constant)
„
Refraction of Light
Reflection of Light; Law of Reflection
„
„
A ray of light, the incident ray,
travels in a medium
When a light ray encounters a
boundary, part of the incident ray
is reflected back
„
„
We deal with specular reflection in
this course
„
„
Law of Reflection
„
„
„
„
normal - line perpendicular to the
surface at the point where the
incident ray strikes the surface
The incident ray makes an angle of
θ1 with the normal
The reflected ray makes an angle
of θ1’ with the normal
The angle of reflection is equal to
the angle of incidence:
θ1= θ1’
When a light ray encounters a
boundary:
„
Specular and diffuse reflection
„
„
A ray of light is an imaginary
line drawn along the direction
of travel of the light beams
A wave front is a surface
passing through points of a
wave that have the same
phase and amplitude
The ray that enters the second
medium is refracted (bent) at the
boundary
„
„
„
part of the ray is reflected
part of the ray enters the second
medium
The incident ray, the reflected ray,
the refracted ray, and the normal all
lie on the same plane
Refracted occurs because the speed
of light is different in the two media
The angle of refraction depends
upon the material and the angle of
incidence:
sin θ12 vv22
sin
=
= constant
sinθθ21 vv1
sin
2
Refraction of Light
„
When a light ray encounters a
boundary:
„
„
„
„
„
„
part of the ray is reflected
part of the ray enters the second
medium
The ray that enters the second
medium is refracted (bent) at the
boundary
„
Refraction of Light
„
„
„
The incident ray, the reflected ray,
the refracted ray, and the normal all
lie on the same plane
Refracted occurs because the speed
of light is different in the two media
The angle of refraction depends
upon the material and the angle of
incidence:
„
„
n=
„
Some values of n
„
„
„
„
„
speed of light in a vacuum c
=
speed of light in a medium v
For a vacuum, n = 1
For other media, n > 1
n is a unitless ratio
As the value of n increases, the
speed of the wave decreases
As light travels from one medium
to another, its frequency does not
change
The incident ray, the reflected ray,
the refracted ray, and the normal all
lie on the same plane
Refracted occurs because the speed
of light is different in the two media
The angle of refraction depends
upon the material and the angle of
incidence:
sin θ12 vv22
sin
=
= constant
sinθθ21 vv1
sin
The Index of Refraction
The index of refraction, n, of a
medium can be defined:
part of the ray is reflected
part of the ray enters the second
medium
The ray that enters the second
medium is refracted (bent) at the
boundary
„
sin θ12 vv22
sin
=
= constant
sinθθ21 vv1
sin
„
When a light ray encounters a
boundary:
Index of Refraction Extended
„
„
„
The frequency remains the same as the
wave travels from one medium to the
other
v=ƒλ
The ratio of the indices of refraction of
the two media can be expressed as
various ratios
c
n1 n2
λ1 v1
=
=
=
c
n1
λ2 v2
n2
3
Snell’s Law of Refraction
Some Indices of Refraction
n1 sin θ1 = n2 sin θ2
„
θ1 is the angle of
incidence
θ2 is the angle of
refraction
„
„
Can derive from
Maxwell equations
„
Problem 22.21, p 755
„
Two light pulses are emitted
simultaneously from a source. The
pulses take parallel paths to a
detector 6.20 m away but one
moves through air and the second
through a block of ice. Determine
the difference in the pulses’ arrival
times at the detector.
22.4: Dispersion
„
The index of refraction in anything except a
vacuum depends on the wavelength of the light
„
This dependence of n on λ is called dispersion
„
„
„
The index of refraction for a material usually
decreases with increasing wavelength (‘normal’
dispersion)
„
„
Dispersion plays a very important role in fiber
optical communications
Snell’s Law indicates that the angle of
refraction made when light enters a material
depends on the wavelength of the light
In ‘anomalous’ dispersion, the index of refraction
increases with increasing wavelength
Violet light refracts more than red light when
passing from air into a material
4
Refraction in a Prism
„
„
The amount the ray is
bent away from its
original direction is
called the angle of
deviation, δ
Since all the colors
have different angles of
deviation, they will
spread out into a
spectrum
„
„
Violet deviates the most
Red deviates the least
5