Download Chapter 32Light: Reflection and Refraction

Chapter 32Light: Reflection and Refraction
HW 6: Chapter 32: Pb.12, Pb.43,
Pb.46
Chapter 33: Pb.14, Pb.27, Pb.29
Due On Friday, April 14.
30-4 LR Circuits
Example 30-6: An LR circuit.
At t = 0, a 12.0-V battery is connected in
series with a 220-mH inductor and a total of
30-Ω resistance, as shown. (a) What is the
current at t = 0? (b) What is the time
constant? (c) What is the maximum current?
(d) How long will it take the current to reach
half its maximum possible value? (e) At this
instant, at what rate is energy being
delivered by the battery, and (f) at what
rate is energy being stored in the inductor’s
magnetic field?
30-5 LC Circuits and
Electromagnetic Oscillations
An LC circuit is a charged capacitor shorted
through an inductor.
30-5 LC Circuits and
Electromagnetic Oscillations
Summing the potential drops around the
circuit gives a differential equation for Q:
This is the equation for simple harmonic
motion, and has solutions
.
.
30-5 LC Circuits and
Electromagnetic Oscillations
Substituting shows that the equation can only
be true for all times if the frequency is given
by
The current is sinusoidal as well:
30-5 LC Circuits and
Electromagnetic Oscillations
The charge and current are both sinusoidal,
but with different phases.
30-5 LC Circuits and
Electromagnetic Oscillations
The total energy in the circuit is constant; it
oscillates between the capacitor and the inductor:
Problem 34
34. (II) A 425-pF capacitor is charged
to 135 V and then quickly connected to a
175-mH inductor. Determine (a) the
frequency of oscillation, (b) the peak
value of the current, and (c) the
maximum energy stored in the magnetic
field of the inductor.
30-6 LC Oscillations with
Resistance (LRC Circuit)
Any real circuit will have resistance
added to the LC.
30-6 LC Oscillations with
Resistance (LRC Circuit)
Now the voltage drops around the circuit
give
31-3 Maxwell’s Equations
This set of equations describe electric and magnetic
fields, and is called Maxwell’s equations. In the absence
of dielectric or magnetic materials, they are:
Gauss’s Law
Gauss’s Law of magnetism
A magnetic field induce a
electric field
General form of Ampere’s law
A electric field induce a magnetic field
31-4 Production of Electromagnetic
Waves
Since a changing electric field produces a
magnetic field, and a changing magnetic field
produces an electric field, once sinusoidal fields
are created they can propagate on their own.
These propagating fields are called
electromagnetic waves (EM).
What is Light?
https://www.youtube.com/watch?v=IXxZRZxafEQ
Induced Electric Fields
• Electric & Magnetic fields induce each other
Changing B induces emf  changing E
Changing E  changing B
 create
electromagnetic waves
Electromagnetic Waves
Charge accelerates:
this creates a changing B-field
By Faraday’s Law of induction
this creates a changing E-field
E
B
31-5 Electromagnetic Waves, and Their
Speed, Derived from Maxwell’s Equations
B and E are related by the following equation
Calculated by Maxwell
.
Here, v is the velocity of the wave.
The magnitude of this speed is around 3.0 x 108 m/s
– precisely equal to the measured speed of light.
Maxwell’s argue that light in EM wave after this
calculation, Hertz showed this experimentally 8 years
later.
Speed of EM Waves -- vacuum
• EM waves do not require a medium to propagate
1
m
c=
= 2.998 ´ 10
s
Î0 m0
8
Permittivity of free
space
= 8.85 x 10-12
C2/Nm2
Permeability of free
space:
= 4 x 10-7 Tm/A
31-6 Light as an Electromagnetic Wave
and the Electromagnetic Spectrum
The frequency of an electromagnetic wave is
related to its wavelength and to the speed of
light:
Speed of Light in matter
• Generally light slows down when it encounters a
medium other than vacuum.
v =
n is the index of
refraction of the
medium n≥1
c
n
c = lof v = lf
l=
v
c
lo =
lo
n
l
l
c
l
v
Frequency is unchanged
n
31-6 Light as an Electromagnetic Wave
and the Electromagnetic Spectrum
Electromagnetic waves can have any wavelength;
we have given different names to different
parts of the wavelength spectrum.
32-1 The Ray Model of Light
Light very often travels in straight lines. We
represent light using rays, which are straight lines
emanating from an object. This is an idealization,
but is very useful for geometric optics.
32-2 Reflection; Image Formation
by a Plane Mirror
Law of reflection: the angle of reflection (that
the ray makes with the normal to a surface)
equals the angle of incidence.
32-2 Reflection; Image Formation
by a Plane Mirror
When light reflects from a rough surface, the law
of reflection still holds, but the angle of incidence
varies. This is called diffuse reflection.
32-2 Reflection; Image Formation
by a Plane Mirror
With diffuse reflection, your
eye sees reflected light at all
angles. With specular
reflection (from a mirror),
your eye must be in the
correct position.
32-2 Reflection; Image Formation
by a Plane Mirror
What you see when you look into a
plane (flat) mirror is an image, which
appears to be behind the mirror.
32-2 Reflection; Image Formation
by a Plane Mirror
This is called a virtual image, as the light
does not go through it. The distance of the
image from the mirror di is equal to the
distance of the object from the mirror d0
32-2 Reflection; Image Formation
by a Plane Mirror
Example 32-1: Reflection from flat mirrors.
Two flat mirrors are perpendicular to each
other. An incoming beam of light makes an
angle of 15° with the first mirror as shown.
What angle will the outgoing beam make with
the second mirror?