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

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 Mon. Feb. 18, 2008

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

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

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

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

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

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

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

Two-slit interference Mon. Feb. 18, 2008

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

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

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

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

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

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

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

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

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

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

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

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

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=10 -> q=10p->p=0.2m Mon. Feb. 18, 2008

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

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

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. Example on board: force between two charged particles 1 m apart with 1 milli-Coulomb of charge each. Mon. Feb. 18, 2008

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

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

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

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

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

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

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

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

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

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