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Exam covers Ch. 21.5-7, 22-23,25-26, Lecture, Discussion, HW, Lab Physics 208 Exam 1 Review Exam 1 is Wed. Feb. 20, 5:30-7 pm, Sections , , , , , 2103 Chamberlin Hall Sections , , , , , 180 Science Hall Chapter 21.5-7, 22 Chapter 23 Chapter 25 Chapters 26 Mon. Feb. 18, 2008 1 Electric charges and forces Electric fields Path length difference and phase Two slit interference Phase change on reflection 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 3 different path length -> phase difference. Alternating max and min due to path-length difference 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 2 Chapter 22: Waves & interference Wavelength, frequency, propagation speed related as "f = v Phase relation Reflection, refraction, and image formation Mon. Feb. 18, 2008 Properties of waves Waves, interference, and diffraction 4 Question You are listening to your favorite radio station, WOLX 94.9 FM (94.9x106 Hz) while jogging toward 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) Path length difference d Phase difference = (d/λ)2π radians Constructive for 2πn phase difference Hint: wavelength = (3x108 m/s)/94.9x106 Hz L λ=3.16 m Shorter path A. 3 m B. 1.6 m Light beam Longer path Foil with two narrow slits Mon. Feb. 18, 2008 C. 0.8 m D. 0.5 m Recording plate 5 Mon. Feb. 18, 2008 d-x x d path length diff = (d-x)-(d+x) = 2x = λ/2 6 1 Two-slit interference Two-slit interference: path length L y θ Constructive int: Phase diff = 2"m, m = 0,±1,±2K Path length diff = m", m = 0,±1,±2K Destructive int. Phase diff = 2" (m + 1/2), m = 0,±1,±2K ! diff = (m + 1/2) ", m = 0,±1,±2K Path length ! Path length difference " d sin # " d ( y /L ) ! d sin $ 2# d Phase difference " 2# " ( y /L) ! Mon. Feb. 18, 2008 7 % Mon. Feb. 18, 2008 % 8 ! ! Thin film interference Reflection phase shift Possible additional phase shift on reflection. Start in medium with n1, reflect from medium with n2 λair 1/2 wavelength phase shift from top surface reflection Reflecting from n2 air: n1 =1 n2>n1, 1/2 wavelength phase shift n2<n1, no phase shift t Difference in phase shift between different paths is important. n2>1 λair/n air: n1 =1 Extra path length No phase shift from bottom interface Reflecting from n1 Extra phase shift needed for constructive interference is (m + 1/2)( "air /n) " 2t = ( m + 1/2)( #air /n ) Mon. Feb. 18, 2008 9 Mon. Feb. 18, 2008 10 ! ! Overlapping diffraction patterns 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. Two independent point sources will produce two diffraction patterns. Angular separation If diffraction patterns overlap too much, resolution is lost. Image to right shows two sources clearly resolved. θ Circular aperture diffraction limited: "min = 1.22 Mon. Feb. 18, 2008 11 Mon. Feb. 18, 2008 # D 12 ! 2 Diffraction gratings Chap. 23: Refraction & Ray optics Diffraction grating is pattern of multiple slits. Very narrow, very closely spaced. Same physics as two-slit interference Refraction Ray tracing Types of images sin " bright = m Lens equation Magnification # d Mon. Feb. 18, 2008 13 ! Real image: project onto screen Virtual image: image with another lens d sin " bright = m#, m = 0,1,2K Can locate image by following specific rays Relates image distance, object distance, focal length Ratio of images size to object size Mon. Feb. 18, 2008 14 ! Lenses: focusing by refraction Refraction Occurs when light moves into medium with different index of refraction. Light direction bends according to n1 sin "1 = n 2 sin " 2 F Object θi,1 θr n1 n2 Special case: Total internal reflection ! Image 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 θ2 Angle of refraction Mon. Feb. 18, 2008 15 Mon. Feb. 18, 2008 Different object positions 16 Question Object P.A. Image (real, inverted) You have a focused image on the screen, but you want the image to be bigger. Relative to the lens, you should A. Move screen away, move object away Image (real, inverted) B. Move screen closer, move object away C. Move screen away, move object closer Image (virtual, upright) Mon. Feb. 18, 2008 D. Move screen closer, move object closer These rays seem to originate from tip of a ‘virtual’ arrow. 17 Mon. Feb. 18, 2008 18 3 Question Equations Image and object different sizes 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? Image (real, inverted) p Relation between image distance object distance focal length Magnification = M = ! A. f~0.1m 1 1 1 + = p q f image height q image distance = = object height p object distance 19 20 ! Charges conductors & insulators Add by superposition Drops off with distance as 1/r2 Charge free to move Distributed over surface of conductor Insulator 21 Like charges repel Unlike charges attract Conductor: Insulators and conductors Polarization of insulators, conductors Mon. Feb. 18, 2008 Two types of charges, + and Total charge is conserved Vector forces between charges Triboelectric effect: transfer charge Charges stuck in place where they are put Mon. Feb. 18, 2008 Equal but opposite charges are placed near a negative charge as shown. What direction is the net force on the negative charge? Electrical force between two stationary charged particles A) Left 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/(4πε o) Directed along line joining particles. 22 Forces add by superposition Electric force: magnitude & direction - B) Right εo = permittivity of free space = 8.854 x 10-12 C2 / N.m2 F= C) Up D) Down E) Zero Mon. Feb. 18, 2008 1 1 1 + = 5.5 = " f = 0.18m 0.2m 2m f Mon. Feb. 18, 2008 Chapter 25: Electric Charges & Forces mag=10 -> q=10p->p=0.2m ! D. f~1.0m ! q=2 m B. f~0.2m C. f~0.5m Mon. Feb. 18, 2008 1 1 1 + = p q f q 23 Mon. Feb. 18, 2008 + kq1q2 r2 - 24 4 Electric field Chapter 26: The Electric Field Defined as force per unit charge (N/C) Calculated as superposition of contributions from different charges Examples Fe = qE If q is positive, F and E are in the same direction Example: electric field from point charge Single charge Electric dipole Line charge, sheet of charge Qp=1.6x10-19 C + Electric field lines Force on charged particles E r = 1x10-10 m E = (9×109 )(1.6×10-19)/(10-10) 2 N = 2.9×1011 N/C Mon. Feb. 18, 2008 25 Pictorial representation of E: Electric Field Lines 27 r 1 2p 3 4 "#o r r r 1 p E =" 4 #$o r 3 -q A. Has a maximum at x=0 B. Has a maximum at x=∞ C. Has a maximum at finite nonzero x ! x D. Has a minimum at finite nonzero x On x-axis far from dipole ! 28 y r Electric dipole p = qs moment +q Mon. Feb. 18, 2008 Electric field from a uniform ring of charge. The magnitude of the electric field on the x-axis On y-axis far from dipole ! 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 Quick quiz: continuous charge dist. Electric dipole r E= 26 Electric field lines Mon. Feb. 18, 2008 (to the right) Mon. Feb. 18, 2008 E. Has neither max nor min Electric field magnitude drops off as 1/r3 Mon. Feb. 18, 2008 29 Mon. Feb. 18, 2008 30 5 Force on charged particle Force on a dipole 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 31 Dipole made of equal + and - charges Force exerted on each charge Dipole Uniform field causes rotation Mon. Feb. 18, 2008 32 Dipole in non-uniform field A dipole is near a positive point charge in a viscous fluid. The dipole will A. rotate CW & move toward charge B. rotate CW & move away C. rotate CCW & move toward + D. rotate CCW & move away E. none of the above Mon. Feb. 18, 2008 33 6