A Brief History of Light
Isaac Newton, 1600s: Light is like little bullets.
Scientists: Okay, right, that makes sense!
Thomas Young, 1800s: No, no, check this out. (Shines
light through two slits.) Interference! Its a wave!
Scientists: Oooooh, youre right
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University of Alberta
Department of Physics
Physics 130 A01/EA01 Midterm Exam
Date: 22 October, 2008 Place: ETLE 1-007
Time: 9:009:50 am Instructor: Dr. R. MacDonald
Name:______________I.D.#
Formula sheet and calculator allowed. Please com
Interference of Two Waves
Fig. 16.21
Remember that wavefunctions add
at each point when they overlap.
Depending on the relative phase
(i.e. the difference in phase) the
waves can add constructively or
destructively at a given point.
If the two waves are a
Multi-Lens Magnication
Theres a limit to the angular magnication you can get
from a simple magnifying lens.
But remember that an image can be treated just like an
object. So you can use two lenses in combination; use
the rst lens to create an image that y
s1
s2
s2
Angular Size
s1
Final
Image
Object
Lens 1
s1
Image 1
(object for Lens 2)
Lens 2
s1
When we look at something, one of our
main clues for determining the size is the
size of the image on the retina; a larger
object will result in a larger image.
ob
Principal Rays
Ray through the centre
Fig. 34.36a
The other thing to know about thin lenses is that a
ray through the middle of the lens comes out
undiverted.
Both sides of the lens are parallel and
approximately at at the centre, so its like a really
thi
Two Types of Lenses
Fig. 34.28a
Fig. 34.31a
Converging
Lens
Diverging
Lens
Focal Points: Converging Lens
Fig. 34.28
If the lens is thicker in the
middle than on the edges,
its a converging lens.
If the lens is thinner in the
middle than on the edges,
its
Relating s to s
Extended Object
g. 34.22
( a) + + =
or:! + = a
( ) + + b =
or:! + b =
Object-image relationship,
spherical refracting surface:
Focal Point
na sina = nb sinb
na a nb b
sin =
h
R
Lateral Magnication: m=y/y
g. 34.22
The focal point is the
Convex Spherical Mirrors
Image should be
behind the mirror, and
the image distance s
should be less than
the object distance s.
Just like with a plane mirror, when
light from an object strikes a
convex mirror it goes off in all
directions; when your eyes
Image Size and Direction: m
g. 34.14
Fig. 34.20d
Lateral magnication,
Spherical mirror
s
m=
s
In this case, this will give a
negative magnication; the
image is inverted.
Relating s to s
Sum of angles in a triangle:
! ( ) + + =
! or:! + =
Fig. 34.10a
Sub
Only works for small angles!
Everything were discussing about
spherical mirrors is only true for
rays that are close to the optic
axis, so that the angles of
reection are small.
These are called paraxial rays,
meaning rays close to the axis.
Focal Point
W
Image Distance: Plane Mirror
The two rays (PB and PV) shown
give where youd see the image
depending on where you look.
Fig. 34.4
Sign Conventions
Sign rule for the object
distance:
When the object is on the
same side of the surface as
the incoming light,
Seeing an Object
6: Geometric Optics
(Chapter 34)
eye
Phys130, A04
Dr. Robert MacDonald
Light rays from each point on the object go
everywhere. Some light from each point reaches the
eye.
2
object
virtual image
eye
eye
When we look in a mirror, the rays t
Diffraction vs Geometry
Geometric optics says that
shadows should always have a
sharp edge if the light is parallel or
from a point source.
8: Diffraction
(Chapter 36)
Thats not what actually happens!
In fact, all shadows have some
blurring.
Phys130, A01
Special Case:
A Clamped String
The wavefunction weve developed for standing
waves, y(x,t) = A sin(kx) sin(t), xes a node at x=0.
Now lets consider what happens if you x the string
at both ends, like youd nd in a guitar, piano, power
line, etc. (Ill refer
Resonance and Sound
We studied forced oscillations previously. It works
the same way with sound in a pipe as it does with a
simple harmonic oscillator.
If you generate a sound with some frequency near the
pipe, the molecules of air in the pipe will oscill
Resonance and Sound
We studied forced oscillations previously. It works
the same way with sound in a pipe as it does with a
simple harmonic oscillator.
If you generate a sound with some frequency near the
pipe, the molecules of air in the pipe will oscill
Longitudinal
Standing Wave
Waves and Pipe Ends
A longitudinal standing wave is
describe just the same as a
transverse wave; the displacement
y of the particle at position x at
time t is given by
!
y(x,t) = Asw sin(kx) sin(t)
At a closed end of a pipe, the
Decibels and Attenuation
What Im describing for the decibel scale is not the
only way its used. Its often useful to use other
reference intensities for various purposes.
Ampliers and attenuators will sometimes list how
much theyre changing the signal in d
Spherical Symmetry
Consider a spherical wave a wave which spreads
out evenly in all directions. This is the kind of wave
you get from a point source of light (bulb, candle,
star), sound, etc.
At a distance r from the source, the energy of the
wave is spre
Speed of Sound in a Fluid
We have an expression for the speed of a wave on a
string:
What does the speed of a wave (sound) in a uid
depend on?
We can expect it has something to do with how
difcult it is to compress the uid; this is described
by the bulk
On Sound
4: Sound Waves
(Chapter 16)
Phys130, A04
Dr. Robert MacDonald
Sound is any longitudinal (compression) wave in a
tangible medium, like air, wood, rock, the sun, etc.
At least some aspects of an earthquake are
essentially huge sounds.
The audible
Mechanical Waves
A mechanical wave is a travelling disturbance in a
medium (like water, string, earth, Slinky, etc).
3: Mechanical Waves
(Chapter 15)
Move some part of the medium out of equilibrium,
and that motion travels (or propagates) from one
place i
Forced Oscillations
If you take a mass on a spring and start it moving, it will
oscillate at some frequency determined by k, m, and b,
and it will eventually stop.
But if you attach the other end of the spring to a motor
instead of something stationary, y
So after all that, we found:
Damped Oscillations
Remember that we identied k = (mg/L). Look familiar?
This is the same form as the potential energy for a mass
on a spring, with k replaced.
(Remember that this is only true for small swings, i.e.
small , sm
Energy in SHM
Energy Conservation
Energy can only transfer between the mass (as kinetic
energy) and the spring (as potential energy). It cant go
anywhere else. So the total energy is
Fig. 13.8b
Consider a cart on a horizontal air track.
Kinetic energy:
Back to the Shadows
Restoring Force Redux
Recall that the acceleration of the
shadow point P is given by
a = aQ cos
unstretched
position
So if aQ = 2A, then
a = 2A cos.
Fs
50 g
But x = A cos!
Fs
So a = 2x.
Fg
Compare with SHM:
Fs < Fg
Theyre the same, if
Boundaries and Reections
Waves reect when they hit a boundary. Youve heard
echoes, and you saw the reections on the stretched
spring in class.
This is just the conservation of energy; the energy has
nowhere to go, so its sent back the way it came.
How exa
Wave Speed vs Particle Speed
Be careful when talking about speeds in waves. There
are two!
The wave is moving along at a constant speed which
depends on the tension and linear density of the string.
Each particle or bit of the string is moving up and down