PHY 2054C Review guide Fall 2018 Chapter 17 Wave optics

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1 PHY 2054C Review guide Fall 2018 Chapter 17 Wave ptics Light acts as a wave, ray, particle, and phtn. Refractive index n = c/v Light waves travel with speed c in a vacuum they slw dwn when they pass thrugh transparent materials such as water r glass r air. Index f refractin is always greater than 1 because v is always less than c. Refractive index f air = 1 (apprx.), vacuum = 1 (exactly) Interference Cnstructive interference Superpsitin f tw r mre waves int a single wave is called interference. The waves are in phase Destructive interference When the waves are ut f phase Thin film interference Interference between waves reflected frm tw surfaces f a thin film with index f refractin n. A wave that reflects frm a surface at which the index f refractin increases has a phase change. Cnstructive and destructive interference is due t verlap f tw r mre waves as they spread behind penings Single slit experiment

2 A single slit f width a has a bright central maximum f width that is flanked by a secndary maxima. Angle fr dark fringes If l/a <<1, then frm the small-angle apprximatin, Yung s duble slit experiment Cnstructive interference differ by a whle number f wavelength. The screen is bright by these pints Destructive interference differ by a whle number f wavelength plus half a wavelength. The screen will be dark at this pint Series f alternating bright and dark bands f light is called interference fringes. The fringes are numbered frm m=0, 1, 2, 3 ging utward frm the center. The brightest fringe at the midpint has m=0 and is called central maximum. L is the distance between duble slit and viewing screen d is the distance between slits Assume L is very much larger than d

3 Frmula fr angle (in radians) f bright fringes fr duble slit interference with split spacing d Fringe spacing between tw adjacent bright fringes Diffractin Spreading f wave after passing thrugh an pening is called diffractin. It spreads ut t fill the space behind the pening. Diffractin grating A multi-slit device creates a pattern n the screen due t the interference f N verlapped waves. N light waves frm N different slits will all be in phase with each ther when they arrive at a pint n the screen at angle qm such that Very bright and narrw fringes are lcated at angles and psitins Chapter 18 Ray ptics Light rays can travel in lines, crss, travel frever unless it interacts with matter. An bject is a surce f light ray. The eyes see by fcusing a bundle f rays enter pupil and fcused n an image n retina. Interactin with matter causes light rays t reflect, refract, scatter, r be absrbed. Light rays cme frm self-luminus r reflective bjects. Each pint n the bject sends rays in all directins. Nte that ray diagrams use nly a few select rays t represent all the rays emitted by an bject. Reflectin Law f reflectin qi = qr

4 Reflectin can be specular (smth) r diffuse (rugh surface) Plane mirrrs: a virtual image is frmed at P with s = s, where s is the bject distance and s is the image distance Refractin Snell s law f refractin: n1sinq1 = n2sinq2 n = c/v hw t determine which material has a larger refractive index? If the refracted ray is clser t the nrmal, that material has larger refractive index than the tp Ttal internal reflectin (TIR) Occurs when n2<n1. When angle f incidence is greater than qc= sin -1 (n2/n1), qc is the critical angle

5 Image frmatin Thin lens equatin quantity psitive negative s always - s Real image (ppsite side f lens/in frnt f mirrr) Virtual image (same side f lens/behind a mirrr) f Cnverging lens r cncave mirrr Diverging lens/cnvex mirrr m Image is upright Image is inverted Magnificatin m = -s /s Chapter 20 Electric Field and Charges Charge: - there are tw kinds f charges, called psitive and negative. Atms are made up f a nucleus that cntains psitively charged prtns that are surrunded by a clud f negatively charged electrns. The fundamental charge e represents the magnitude f the charge n an electrn r prtn: e = 1.60 x Matter with equal amunts f psitive and negative charge is neutral

6 Charge is cnserved; it can t be created r destryed*** Culmb s Law: - The frces between tw charged particles q1 and q2 separated by distance r are F " $% & = F & $% " = K q " q & r & Where K = 8.99 x 10 9 N * m 2 /C 2 is the electrstatic cnstant. These frces are an actin/reactin pair directed alng the line jining the particles. The frces are repulsive fr tw charges that are same, attractive fr tw ppsite charges The net frce n a charge is the vectr sum f the frces frm all ther charges. The unit f charge is the culmb (C). The Electric Field: - Charges interact with each ther via the electric field, Charge A changes the space arund it by creating an electric field. The field is the agent that exerts a frce n charge B. An electric field is identified and measured in terms f the frce n a prbe charge q. The unit f the electric field in N/C. The electric field is a vectr. The electric field frm multiple charges is the vectr sum f the fields frm the individual charges. Visualizing the electric field: - The electric field exists at all pints in space. An electric field vectr shws the field at nly ne pint, the pint at the tail f the vectr. A field diagram shws field vectrs at several pints. Electric field lines:

7 are always parallel t the field vectrs are clse where the field is strng, far apart where the field is weak. G frm psitive t negative charges. There are tw types f material, insulatrs and cnductrs. Charge tends t remain fixed n an insulatr. Charge is able t mve easily thrugh cnductrs. Charge is transferred by cntact between bjects. A diple has n net charge but has a field because the tw charges are separated. A diple will rtate t align with an electric field. Electric fields: imprtant cases The electric field f a pint charge is = ( K q, [away frm q if q > 0, tward q if q < 0], r & The electric field inside a parallel-plate capacitr is unifrm: = ( Q, frm psitive t A N"& OP = 8.85 x 10 Q m& is the permittivity cnstant. Cnductrs in electric fields: -

8 The electric field inside a cnductr in electrstatic equilibrium is zer. Any excess charge is n the surface. The electric field is perpendicular t the surface. The density f charge and the electric field are highest near a pinted end. Chapter 21 Electric Ptential Electric Ptential and Ptential Energy: - The electric ptential V is made up f charges and is fund at every pint that surrunds thse charges When a charge q is brught clser t these charges, it acquires an electric ptential energy at a pint where the ther charges have created an electric ptential V. Energy is cnserved fr a charged particle in an electric ptential: K S + qv S = K V + qv V r K = q V Surces f Ptential: - Ptential differences V are created by a separatin f charge. There are tw main surces f ptential difference

9 A battery, which separates charges using chemicals and is able t create a ptential difference The ppsite charges n the plates f a capacitr, which creates a ptential difference between the plates. The electric ptential f a pint charge q is V = K Y Z Cnnecting ptential and field: - Fr a cnductr in electrstatic equilibrium Any excess charge is n the surface. The electric field inside is zer The exterir electric field is perpendicular t the surface. The field strength is largest at sharp crners The entire cnductr is at the same ptential and s the surface is an equiptential. Capacitrs and dielectrics: - The charge ±Q n tw cnductrs and the ptential difference V \ between them are prprtinal: Q = C V \

10 where C is the capacitance f the tw cnductrs. A parallel-plate capacitr with plates f area A and separatin d has a capacitance C A/d When a dielectric is put in between the plates f a capacitr, the capacitance increases by a factr K, the dielectric cnstant f the material. The energy stred in a capacitr is U O = " & C( V O) &. This energy is stred in the electric field and energy density f u, = 1 2 E & Parallel-plate capacitr: - Fr a capacitr charged t V \ the ptential at distance x frm the negative plate is The electric field inside is E = V \ /d V = x d V \ UNITS: - Electric ptential: 1 V= 1 J/C Electric field: 1 V/m = 1 N/C Energy: 1 electrn vlt = 1 ev = 1.60 x J. This is the kinetic energy that is gained when an electrn accelerates thrugh a ptential difference f 1 V. Chapter 22 Current and Resistance Battery is a surce f ptential difference. Chemical prcess separate charges. The ptential difference f battery is called emf (electrmtive frce). This ptential difference create electric field that drives the current. Nte that there is cnservatin f current in the circuit. Law f cnservatin f current Current is same at all pints in a current carrying wire

11 Resistance Measure f hw hard it is t push against charges Resistivity Resistance f a wire depends n the material it is made up f Resembled by Greek letter rh, r Characterizes electrical prperties f material Gd cnductrs have lw resistivities Pr cnductrs have high resistivities Ohm s law D I = V R wire Relatinship between current, vltage, and resistance Measured in hms Current is directly prprtinal t ptential difference Energy and pwer Emf supplies the energy used by a circuit thrugh a series f transfrmatin. E chemical energy -> U electric energy àk à E thermal energy Battery supplies pwer at the rate Resistr dissipates pwer at the rate Chapter 23 Circuits DC Current Resistrs cnnected in series A series cnnectin has n junctin T calculate equivalence resistance f resistrs cnnected in series R = R + R eq 1 2 Capacitrs in series T calculate capacitance equivalence in series

12 Resistrs cnnected in parallel Parallel in cnnectin has junctin T calculate equivalence resistance f resistrs cnnected in parallel Capacitrs in parallel T calculate capacitance equivalence in parallel Kirchff s law Lp rule Assign a directin t the current Add ptential differences arund the lp Junctin law Junctin rule frmula RC Circuits Discharge f a capacitr thrugh a resistr is an expnential decay

13 t / ( ) - D V = DV e t C C 0 Time cnstant t = RC Chapter 24 Magnetic Fields and Frces Magnetic field can be created by either electric current r permanent magnet Magnetic diple cnsists f a nrth ple and suth ple Unlike ples attract, like ples repel each ther Parallel wires with currents in the same directin attract each ther; when the currents are in ppsite directins, the wires repel each ther Magnetic field and frces Magnetic field is measured in Tesla (T). Right hand rule Directin f magnetic field -6 µ 0 = T m/a Directin f frce

14 Magnetic frce frmula Magnitude f frce n a current carrying wire F = ILB Trque n a current lp in a magnetic field depends n current, lp s area, hw the lp is riented in the field Chapter 25 EM Inductin and EM Waves Magnetic flux 1Wb= 1T m Measures the amunt f magnetic field passing thrugh a surface 2 Lenz s law Induced current in a clsed cnducting lp if magnetic flux thrugh the lp. The directin f induced current is such that induced magnetic ppses the change in flux.

15 Faraday s law Magnitude f the induced emf in a clsed lp e Multiply by N fr an N-turn cil DFper cil e cil = N Dt The size f the induced current is EM wave Oscillating electric and magnetic field Speed f prpagatin f wave 1 v = Mtinal emf DF = D t I induced em e = R Î µ v em = m/s Mtin f cnductr thrugh a magnetic field prduces a frce n the charges. The separatin f charges leads t an emf Phtn mdel Energy f a phtn f frequency f is Planck s cnstant E = hf -34 h = J s phtn - Electrmagnetic spectrum

16 Chapter 26 AC Electricity AC circuits Driven by emf that scillates with frequency I,V = peak current, peak vltage i, v = instantaneus current, instantaneus vltage Pwer Elements used in AC circuit Inductive reactance 1 henry = 1 H = V s / A Capacitative reactance Transfrmers X = ( pfl) L 2 X C 1 = 2p fc

17 Increase/decrease vltage Primary is related t secndary LC and RLC circuit The scillatins decay as energy is dissipated in the resistr Resnance frequency f 0 1 = 2p LC Peak current at any frequency f is given by