1. Physics 208 Exam 1 Review
Mon. Feb. 18, 2008 1

2. Exam covers Ch. 21.5-7, 22-23,25-26, Lecture, Discussion, HW, Lab
Exam 1 is Wed. Feb. 20, 5:30-7 pm, Ch: Adam(301,310), Eli(302,311), Stephen(303,306), 180 Science Hall: Amanda(305,307), Mike(304,309), Ye(308)
Chapter , 22
Waves, interference, and diffraction
Chapter 23
Reflection, refraction, and image formation
Chapter 25
Electric charges and forces
Chapters 26
Electric fields
Mon. Feb. 18, 2008

3. Quick Quiz accelerates left accelerates right stays fixed
An electric dipole is in a uniform electric field as shown. The dipole
Dipole
accelerates left
accelerates right
stays fixed
accelerates up
none of the above
Mon. Feb. 18, 2008

4. Electric torque on dipoles
Remember torque?
Here there are two torques, both into page:
Talk about result of torque on dipole: in vacuum, will rotate full one way, then back the other, I.e. oscillate. When damped, it will eventually align with dipole moment aligned to field direction.
Explain here about sense of dipole moment direction.
Total torque is sum of these
Torque on dipole in uniform field
Mon. Feb. 18, 2008

5. Dipole in non-uniform field
A permanent dipole is near a positive point charge in a viscous fluid. The dipole will +
rotate CW & move toward charge
rotate CW & move away
rotate CCW & move toward
rotate CCW & move away
none of the above
Mon. Feb. 18, 2008

6. Properties of waves
Wavelength, frequency, propagation speed related as
Phase relation
In-phase: crests line up
180˚ Out-of-phase: crests line up with trough
Time-delay leads to phase difference
Path-length difference leads to phase difference
Mon. Feb. 18, 2008

7. Chapter 22: Waves & interference
Path length difference and phase
different path length -> phase difference.
Two slit interference
Alternating max and min due to path-length difference
Phase change on reflection
π phase change when reflecting from medium with higher index of refraction
Interference in thin films
Different path lengths + reflection phase change
Mon. Feb. 18, 2008

8. Path length difference
Path length difference d
Phase difference = (d/)2π radians
Constructive for 2πn phase difference L
Shorter path
Longer path
Light beam
Recording plate
Foil with two narrow slits
Mon. Feb. 18, 2008

9. Hint: wavelength = (3x108 m/s)/94.9x106 Hz
Question
You are listening to your favorite radio station, WOLX 94.9 FM (94.9x106 Hz) while jogging away from a reflecting wall, when the signal fades out. About how far must you jog to have the signal full strength again? (assume no phase change when the signal reflects from the wall)
Hint: wavelength = (3x108 m/s)/94.9x106 Hz
=3.16 m
3 m
1.6 m
0.8 m
0.5 m d x
d-x
path length diff = (d+x)-(d-x)= 2x
Destructive 2x=/2x=/4
Constructive make 2x=x=/2
x increases by /4 = 3.16m/4=0.79m
Mon. Feb. 18, 2008

10. Two-slit interference
Mon. Feb. 18, 2008

11. Two-slit interference: path lengthy L 
Constructive int:
Phase diff = Path length diff =
Destructive int.
Phase diff = Path length diff =
Path length difference
Phase difference
Mon. Feb. 18, 2008

12. Reflection phase shift
Possible additional phase shift on reflection.
Start in medium with n1, reflect from medium with n2
n2>n1, 1/2 wavelength phase shift
n2<n1, no phase shift
Difference in phase shift between different paths is important.
Mon. Feb. 18, 2008

13. Thin film interference
air
1/2 wavelength phase shift from top surface reflection
air: n1=1
Reflecting from n2
air/n
No phase shift from bottom interface
n2>1 t
Reflecting from n1
air: n1=1
Extra phase shift needed for constructive interference is
Extra path length
Mon. Feb. 18, 2008

14. Diffraction from a slit
Each point inside slit acts as a source
Net result is series of minima and maxima
Similar to two-slit interference.
Mon. Feb. 18, 2008

15. Overlapping diffraction patterns
Two independent point sources will produce two diffraction patterns.
If diffraction patterns overlap too much, resolution is lost.
Image to right shows two sources clearly resolved.
Angular separation 
Circular aperture diffraction limited:
Mon. Feb. 18, 2008

16. Diffraction gratings Diffraction grating is pattern of multiple slits.
Very narrow, very closely spaced.
Same physics as two-slit interference
Mon. Feb. 18, 2008

17. Chap. 23: Refraction & Ray optics
Ray tracing
Can locate image by following specific rays
Types of images
Real image: project onto screen
Virtual image: image with another lens
Lens equation
Relates image distance, object distance, focal length
Magnification
Ratio of images size to object size
Mon. Feb. 18, 2008

18. Special case: Total internal reflection
Refraction
Occurs when light moves into medium with different index of refraction.
Light direction bends according to
i,1 r
Special case: Total internal reflection n1 n2 2
Angle of refraction
Pont out interface, and refracted and reflected beam
Mon. Feb. 18, 2008

19. Lenses: focusing by refraction
Image
P.A.
Object F
1) Rays parallel to principal axis pass through focal point.
2) Rays through center of lens are not refracted.
3) Rays through F emerge parallel to principal axis.
Here image is real, inverted, enlarged
Mon. Feb. 18, 2008

20. Different object positions
Image (real, inverted)
Object
Image (real, inverted)
Image (virtual, upright)
These rays seem to originate from tip of a ‘virtual’ arrow.
Mon. Feb. 18, 2008

21. Question Move screen away, move object away
You have a focused image on the screen, but you want the image to be bigger. Relative to the lens, you should
Move screen away, move object away
Move screen closer, move object away
Move screen away, move object closer
Move screen closer, move object closer
Mon. Feb. 18, 2008

22. Equations Magnification = M = Image and object different sizes
Image (real, inverted)
Image and object different sizes p q
Relation between image distance object distance focal length
Magnification = M =
Mon. Feb. 18, 2008

23. Question f~0.1m f~0.2m f~0.5m f~1.0m
You want an image on a screen to be ten times larger than your object, and the screen is 2 m away. About what focal length lens do you need?
f~0.1m
f~0.2m
f~0.5m
f~1.0m
q=2 m
mag= > q=10p->p=0.2m
Mon. Feb. 18, 2008

24. Chapter 25: Electric Charges & Forces
Triboelectric effect: transfer charge
Total charge is conserved
Vector forces between charges
Add by superposition
Drops off with distance as 1/r2
Insulators and conductors
Polarization of insulators, conductors
Mon. Feb. 18, 2008

25. Charges conductors & insulators
Two types of charges, + and -
Like charges repel
Unlike charges attract
Conductor:
Charge free to move
Distributed over surface of conductor
Insulator
Charges stuck in place where they are put
Comment that this is pretty amazing.
Show that interaction decreases with distance.
What is the interaction between these electric charges? Mention modern field-theory view.
Mon. Feb. 18, 2008

26. Electric force: magnitude & direction
Electrical force between two stationary charged particles
The SI unit of charge is the coulomb (C ), µC = 10-6 C
1 C corresponds to 6.24 x 1018 electrons or protons
ke = Coulomb constant ≈ 9 x 109 N.m2/C2 = 1/(4πeo)
eo  permittivity of free space = x C2 / N.m2
Directed along line joining particles.
Example on board: force between two charged particles 1 m apart with 1 milli-Coulomb of charge each.
Mon. Feb. 18, 2008

27. Forces add by superposition
Equal but opposite charges are placed near a negative charge as shown. What direction is the net force on the negative charge?
Left
Right Up
Down
Zero - + -
Mon. Feb. 18, 2008

28. Chapter 26: The Electric Field
Defined as force per unit charge (N/C)
Calculated as superposition of contributions from different charges
Examples
Single charge
Electric dipole
Line charge, sheet of charge
Electric field lines
Force on charged particles
Mon. Feb. 18, 2008

29. Example: electric field from point charge
Fe = qE
If q is positive, F and E are in the same direction
Example: electric field from point charge +
r = 1x10-10 m
Qp=1.6x10-19 C E
E = (9109)(1.610-19)/(10-10)2 N = 2.91011 N/C
(to the right)
Mon. Feb. 18, 2008

30. Pictorial representation of E: Electric Field Lines
After field lines up ask to compare efield at two points of equal distance
Mon. Feb. 18, 2008

31. Electric field lines Local electric field tangent to field line
Density of lines proportional to electric field strength
Fields lines can only start on + charge
Can only end on - charge (but some don’t end!).
Electric field lines can never cross
Ask why electric field lines can never cross.
Mon. Feb. 18, 2008

32. Electric dipole Electric field magnitude drops off as 1/r3
On y-axis far from dipole
Electric dipole moment +q
On x-axis far from dipole -q
Electric field magnitude drops off as 1/r3
Mon. Feb. 18, 2008

33. Quick quiz: continuous charge dist.
Electric field from a uniform ring of charge. The magnitude of the electric field on the x-axis y x
Has a maximum at x=0
Has a maximum at x=
Has a maximum at finite nonzero x
Has a minimum at finite nonzero x
Has neither max nor min
Mon. Feb. 18, 2008

34. Force on charged particle
Electric field produces force qE on charged particle
Force produces an acceleration a = FE / m
Uniform E-field (direction&magnitude) produces constant acceleration if no other forces
Positive charge accelerates in same direction as field
Negative charge accelerates in direction opposite to electric field
Mon. Feb. 18, 2008

35. Force on a dipole Dipole made of equal + and - charges
Force exerted on each charge
Uniform field causes rotation
Dipole
Mon. Feb. 18, 2008

36. Dipole in non-uniform field
A dipole is near a positive point charge in a viscous fluid. The dipole will +
rotate CW & move toward charge
rotate CW & move away
rotate CCW & move toward
rotate CCW & move away
none of the above
Mon. Feb. 18, 2008