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Physics 208 Exam 1 Review

Physics 208 Exam 1 Review. Exam covers Ch. 21.5-7, 22-23,25-26, Lecture, Discussion, HW, Lab. Exam 1 is Wed. Feb. 20, 5:30-7 pm, 2103 Ch: Adam(301,310), Eli(302,311), Stephen(303,306), 180 Science Hall: Amanda(305,307), Mike(304,309), Ye(308). Chapter 21.5-7, 22

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Physics 208 Exam 1 Review

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  1. Physics 208 Exam 1 Review

  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, 2103 Ch: Adam(301,310), Eli(302,311), Stephen(303,306), 180 Science Hall: Amanda(305,307), Mike(304,309), Ye(308) • Chapter 21.5-7, 22 • Waves, interference, and diffraction • Chapter 23 • Reflection, refraction, and image formation • Chapter 25 • Electric charges and forces • Chapters 26 • Electric fields

  3. Quick Quiz 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

  4. Electric torque on dipoles Remember torque? • Total torque is sum of these Here there are two torques, both into page: • Torque on dipole in uniform field

  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

  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

  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

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

  9. x d-x d 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) =3.16 m Hint: wavelength = (3x108 m/s)/94.9x106 Hz 3 m 1.6 m 0.8 m 0.5 m 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

  10. Two-slit interference

  11. L y Path length difference Phase difference Two-slit interference: path length  Constructive int: Phase diff = Path length diff = Destructive int. Phase diff = Path length diff =

  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.

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

  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.

  15. Overlapping diffraction patterns Angularseparation • 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.  Circular aperture diffraction limited:

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

  17. Chap. 23: Refraction & Ray optics • Refraction • 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

  18. Special case:Total internal reflection i,1 r n1 n2 2 Angle of refraction Refraction • Occurs when light moves into medium with different index of refraction. • Light direction bends according to

  19. Lenses: focusing by refraction Image F 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

  20. Image (real, inverted) Object Image (real, inverted) Image (virtual, upright) These rays seem to originatefrom tip of a ‘virtual’ arrow. Different object positions

  21. Question • 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

  22. Image (real, inverted) Equations Image and object different sizes • Magnification = M = p q Relation between image distanceobject distancefocal length

  23. Question • 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=10 -> q=10p->p=0.2m

  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

  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

  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 = 8.854 x 10-12 C2 / N.m2 • Directed along line joining particles.

  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 - + -

  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

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

  30. Pictorial representation of E: Electric Field Lines

  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

  32. On y-axis far from dipole Electric dipole moment On x-axis far from dipole Electric dipole • Electric field magnitude drops off as 1/r3 +q -q

  33. x Quick quiz: continuous charge dist. Electric field from a uniform ring of charge. The magnitude of the electric field on the x-axis y 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

  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

  35. Force on a dipole • Dipole made of equal + and - charges • Force exerted on each charge • Uniform fieldcauses rotation Dipole

  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

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