MCAT ExamKrackers Physics Notes
MCAT ExamKrackers Physics Notes
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Date Created: 01/30/14
EaXAMKRACKERS PHYSICS NOTES When multiplying two vectors 0 Vproduct VlV2sintheta o In multiplying two vectors the resultant vector will be perpendicular to both vector 1 and vector 2 O Hsintheta AHcostheta Average velocity is independent of the path chosen In a displacement vs time graph the area undemeath the graph has NO MEANING Linear motion equations could only be used on the straight portions of displacementvstime graphs since these are the only points wherein acceleration is constant In terms of a velocityvstime graph the slope represents the acceleration of the object If one takes the area of the portion between the curve and zero on a velocityvstime graph the area is equal to the distance If one takes the area of the portion below the zero velocity as negative the total area represents displacement To calculate the displacement on a velocityvstime graph one must take the area undemeath the xaxis and subtract it from the area above the xaxis A projectile continues its motion by virtue of its own inertia In projectile motion since there is no acceleration in the horizontal direction this means there is NO CHANGE in horizontal velocity throughout the ight Peak height of a projectile o VsinthetaSquare root2gh I G l0m2quot2 That s POSITIVE 10 I This same equation with replacing v nal for vinitial may be used to nd the nal velocity of a projectile dropped from a certain height h 3e4 With a projectile wherein air resistance is ignored or negligible the path the projectile takes is independent of the mass of the projectile In projectile motion height is dictated only by the vertical velocity 0 Horizontal range is dictated by both horizontal and vertical velocities In projectile motion if two projectiles leave the earth with the same vertical velocity they will land at the same time regardless of their horizontal velocities o A bullet shot horizontally from a gun and a rock dropped from the same height will land at the same time Factors that alter air resistance 0 Speed 0 Surface area 0 Shape Mass changes the effect of air resistance but does not change air resistance Maximum velocity is reached when all gravitational potential energy is 0 and is being converted to kinetic energy generally this is before an object dropped hits the ground Always remember that displacement is a vector For example if two balls are dropped down ramps of l m each but one ramp is vertical while the other is inclined at 30 degrees then their displacements are NOT equal Even though both may travel lm they are travelling at different directions Therefore their displacements are different Objects streamlined with smooth surfaces experience less air resistance than irregularly shaped objects At terminal velocity acceleration is 0 Larger masses experience less deceleration due to air resistance because they are less affected by the same force of air resistance AIR RESISTANCE HAS LESS EFFECT ON THE MORE MASSIVE OBJECT Use bowling ball and bowling pins air molecules example When an graph is multiplied by a negative constant it is re ected over the xaxis If a system is not uniformly dense then the center of mass lies in the more dense area from its geometric center With the universal law of gravitation the movement of the force vector is from the center of one mass towards the center of the other mass In an ideal inclined plane the normal force is always equal to mgcostheta o This works regardless of the angle of the plane 0 The net force due to JUST gravity and normal force is always mgsintheta Normal force along a curved surface 0 Mgcosthetamvquot2r An object on a frictionless incline with an angle between 0 and 90 will accelerate at some fraction of g Most centripetal force problems on the MCAT may be solved via equating the centripetal force to the force responsible for it A satellite is constantly falling towards earth via its centripetal force due to gravity of the earth but due to its massive velocity it always misses the ground by the same distance Thus to someone in circular orbit falling with the satellite it appears to be oating when in fact it is not El sine cosine ij on X1 2 U 1 3O 1 7 0 0 E 45 3 T 1 X3 60 2 TlI 4 90 T2 Kinetic friction coef cientnormal force Static friction is less than or equal to coef cientnormal force To determine whether or not a system is sliding down its contiguous surface nd the calculated net force without friction If it is less than coef cient of static frictionnormal force then the system is probably not moving The negative sign in Hooke s law can usually be ignored of the MCAT but just in case don t forget that it s there The point where an object violates Hooke s law is called the yield point The point where it breaks is called the fracture point For any system IN EQUILIBRIUM the upward force downward force and the leftward force rightward force THIS METHOD ALLOWS YOU TO USE ALL POSITIVE NUMBERS EVEN FOR GRAVITY o The net force acting on a system in equilibrium is 0 which makes sense because if there is constant velocity this means there is no acceleration which by Newton s second law means that there is no net force By MCAT de nition torque is a twisting force Lever arm is a position vector extending from the point of rotation to the vector of force which would cause the angle between these two vectors to be 90 degrees In torque problems if one would like the board to be in static equilibrium then one chooses the board as the system 1 Joule lkgmquot2squot2 o Joules are used for macroscopic objects whereas electronvolts are used for microscopic objects The universe is considered an isolated system Conservative forces do not alter temperature or intemal energy Nonconservative forces include kinetic energy and the pushingpulling applied by humans or animals For conservative forces 0 0change in potential energy change in kinetic energy 0 Conservative forces do not do work For nonconservative forces 0 Work change in kinetic energy change in potential energy Forces that are 90 degrees to the displacement such as normal force or gravity with an item moving horizontally do not do work Greater work manifests itself by greater acceleration greater velocity and less time required to achieve the displacement POWER is a scalar quantity Momentum of an isolated system is always conserved The momentum of the center of mass of an isolated system is constant in magnitude and in direction In elastic collisions Hooke s law is followed perfectly whereas in inelastic collisions it is not with an inelastic collision momentum is conserved BUT kinetic energy is dissipated into intemal energy In a multidimensional system there are two equations for conservation of momentum one for momentum in the Xdirection and one for momentum in the ydirection Airbags do not decrease momentum but they do increase the time over which the collision occurs so that less force is exerted upon the driver In a forcevstime graph the area under the graph represents change in momentum IMPULSE All that machines do is reduce the force necessary to do work THEY DO NOT REDUCE THE WORKLOAD Nonideal machines actually increase the workload because they increase intemal energy through friction Levers are the machines with fulcrums with a pulley F T and 2T mg We multiply the tension here by 2 because pulleys have 2 stringsropes not just one In order to overcome the force pushing an object down an inclined plane one must overcome Fdsintheta which is the force which is pushing the mass down In modi ed levers which look like pulleys the tension is not the same throughout as it would be with a regular pulley Pulleys ramps and levers act under the same principle they increase the distance over which work is to be done effectively reducing the force In dealing with pulley problems choose the pulley as the system DO NOT USE THE MASS AS THE SYSTEM With pulleys and levers the goal is to accomplish dynamic equilibrium with the objects moving upward at a constant velocity meaning there is no net force or acceleration acting upon them On a ramp W mgh ALL machines decrease the force necessary to accomplish a task These machines could be ideal or nonideal with nonideal machines making the work increase Radioactive decay concems atoms which spontaneously break apart 0 All atoms other than hydrogen are subject to such decay Radioactivity may be predicted by protonzneutron ratio and no atoms with greater than 83 protons are considered stable All radioactivity questions only concem 4 variables 0 Amount of half lives 0 Length of half lives 0 Initial amount of substance 0 Final amount of substance 5 types of radioactive decay 0 Alpha decay 0 Beta decay o Positron emission 0 Electron capture 0 Gamma ray emission In alpha decay an alpha particle is lost Beta decay is creation of an electron and a proton from a neutron and the expulsion of the newly created electron INCREASE ATOMIC NUMBERBY l A neutrino is a virtually massless particle also emitted during beta decay In positron emission a proton is transformed into a neutron and a positron is emitted The atomic number goes down by l DECREASE THE ATOMIC NUMBER AND KEEP THE ATOMIC WEIGHT THE SAME 0 Positive electron is written AFTER the arrow Electron capture is the capture of an electron along with the merging of that electron with a proton to create a neutron Thus a proton is destroyed and a neutron is created o DO THE SAME MATHEMATICALLY AS WITH THE POSITRON EMISSION SINCE BOTH ARE BETA DECAY AND KEEP ATOMIC WEIGHT THE SAME WHILST DECREASING THE ATOMIC NUMBER BY 1 0 Negative electron is written BEFORE the arrow and a gamma particle is also released A gamma ray is a high frequency photon It has no charge and does not change the identity of the atom om which it is emitted Gamma decay accompanies other types of decay o For example when electrons and positrons collide which is called ANNIHILATION and deals with matterantimatter Emcquot2 gives the rest mass energy of an object o Latent energy of an object 0 Will only be tested if energy is created or destroyed o mthe mass which is created or destroyed Also referred to as the mass defect nucleon proton neutron ssion and ision both release large amounts of energy and this energy is released due to the mass defect the most stable nuclei have the strongest binding energies Both ssion and ision produce nuclei which are more stable a uid is a liquid or a gas in a uid any existing molecular bonds are constantly breaking and reforming due to the high kinetic energy of the molecules the only permanent force which a uid can exert is one normal to its surface gravity has an insigni cant effect on gas molecules due to their high average velocities two intensive properties in dealing with uids are density analogous to mass and pressure analogous to energy often in dealing with uid mechanics an assumption is made which states that this uid is incompressible This is because when a uid is compressed its volume changes without changing its mass thus changing the density which is generally a dif culty in solving problems speci c gravity density of substancedensity of water DENSITY OF WATER l000kgmquot3 amp lgcmquot3 Fluid pressure results om the impulse of molecular collisions o PFA Fluid pressure is a measure of kinetic energy due to random velocities within a uid distributed over the uid volume Atmospheric pressure 101000 Pascals Gauge pressure measure of pressure compared to the pressure of the local atmosphere Absolute pressure gauge pressure atmospheric pressure Pressure applied anywhere in an enclosed incompressible uid is distributed evenly undiminished throughout the uid Hydraulic lift is a machine that works by Pascal s principle while reducing force necessary for a certain workload to be completed Buoyant force is the upward force acting on a submerged object and is equal to the weight of the uid displaced by the object Does not change with depth Pressure difference densitygravitydifference in height A illy submerged object displaces its volume in uid A oating object displaces its weight in uid If an object is not uniformly dense the center of mass and center of buoyancy will not coincide The object would experience a torque and spin Buoyant force densityvolume displacedgravity A oating object displaces an amount of uid equal to its own weight 0 Fraction submerged density of oating objectdensity of medium in which object is oating Pressure depends only on depth and density not the shape of the container Viscosity is the measure of a uid s temporal resistance to forces not perpendicular to its surface When one says a uid is incompressible this means it has uniform density Mass ow rate I densityVolume ow rate densityareavelocity Uniform translational KE in a uid is achieved by borrowing some energy from the random translational kinetic energy thus causing pressure to decrease For a uid lled container with a spigot opening one can use velocity square root of 2gh to nd velocity Velocity and pressure are inversely proportional A streamline is a path followed by a hypothetical particle o The velocity of a particle along any point of a streamline is tangent to the curve made by the streamline o The magnitude of velocity is inversely related to the distance between the streamlines 0 That is the closer the streamlines the greater the velocity with a real uid the velocity is greater in the innermost part of the tube which is irthest away from the edges This is because the innermost uid particles experience much less drag than the ones on the outside This is why dust remains on fans even though the fan is moving at high speed there is a lot of drag on the edges of the fan surface area 2pird volume dpirquot2 the driving force behind the ow of a uid is the uid s tendency to nd its greatest entropy if for example a needle is oating on the surface of water it is not supported by buoyant force but rather by surface tension of the water a sphere has the lowest surface area volume ratio of any shape surface tension depends on the temperature of the uid in a test tube if the cohesive forces of the uid is stronger than the adhesive forces between the uid and the tube then the uid forms a convex shaped meniscus and is pulled down the tube if adhesive forces are stronger than the cohesive forces the uid forms a concave meniscus and is pulled upward via capillary action For ideal ow volume ow rate is constant at all points Stress ForceArea but the units are Nmquot2 Strain change in dimensionoriginal dimension and has no units since it is a ratio Modulus of elasticity stressstrain An object s maximum elasticity is called the yield point wherein the object will regain its shape once stress is removed Beyond the yield point the object will remain intact but not in its original shape Young s modulus works for tensile compression amp tensile stretching forces Young s modulus E Shear stress modulus G Bulk stress modulus B Modulus stressstrain for elasticity Young s modulus o EFAchange in heightoriginal height Shear stress modulus o G FAchange in x directionoriginal height Bulk stress modulus o B change in pressurechange in volumeoriginal volume 6cmquot2 6 10 4 mquot2 Mechanical waves require some medium through which to travel Nondispersive medium one through which a wave maintains its shape and does not disperse as it travels Waves on a string are transverse waves Sound waves are longitudinal waves For a transverse wave the sine function represents the vertical displacement of the medium with respect to the time or displacement of the wave For longitudinal waves the sine inction represents either change in pressure or horizontal displacement of the medium with respect to time or displacement of the wave The product of wavelength and frequency is the velocity of the wave The period is the number of seconds required for one wavelength to pass a certain point Amplitude A is maximum displacement FROM 0 and is always positive The velocity of a wave is dictated by the medium through which it travels A change in frequency or wavelength does not change the velocity of the wave in a nondispersive medium Two aspects of a medium which in uence velocity of a wave 0 Elastic component tendency of the medium to resist a change in shape I Stores potential energy 0 Inertial component tendency of the medium to resist a change in motion I Stores kinetic energy In a sound wave 0 Velocity square root Bdensity where B is the bulk stress modulus Within a gas the greater the temperature the greater the random velocity the greater the sound wave velocity Because solids are less compressible than gases this means solids have a higher bulk modulus In surface waves gravity acts as the elastic component and they are neither completely transverse nor completely longitudinal Intensity increases with the square of the amplitude and the square of the frequency for all waves B l0logII0 where B is the decibels With decibels if one adds 2 zeros to the intensity one adds 20 decibels If one adds 3 zeros to the intensity one adds 30 decibels Adding 20 decibels is multiplying the intensity by l0quot2 Adding 30 decibels is multiplying the intensity by l0quot3 Adding 10 decibels is multiplying intensity by 10 The phase of a wave relates to wavelength frequency and placetime of origin Each wavelength represents 360 degrees Phase constant the angle by which 2 waves differ If 2 waves of the same wavelength reach the same point but travel different distances to get there then they are out of phase with each other Interference superposition of waves which may be constructive or destructive After passing through each other waves that interfere will revert to their original shape unaffected by the interference Beats occur when 2 waves of slightly different frequencies are superimposed Beat frequency ABSOLUTE VALUE OF FlF2 Pitch correlates to frequency Any refracting wave will continue with the same orientation and same frequency but with a smaller amplitude and a different wavelength from the original medium If the original medium is less dense than the second medium the wave is inverted If original medium is denser than the second medium the wave s orientation remains upright When a wave is transferred from one medium to another the wavelength changes but the frequency stays the same Standing wave when string moves violently up and down at antinodes where maximum constructive interference occurs and does not move at all at nodes where the two waves collide Harmonic series a list of the wavelengths from largest to smallest of the possible standing waves for a given situation The longest wavelength creates the rst harmonic which has the smallest number of nodes 2 Each successive node added creates the subsequent harmonic For a harmonic series where each end is tied down as a node or where each end is an antinode the equation is o Lnlambda2 where L is the distance between the 2 ends of the string For a harmonic series where a string or pipe is only tied down or open at one end that is it has one node and one antinode the equation changes to o L nlambda4 and the n can only be an odd number V f lambda for any harmonic If an outside driving force is applied to a structure at natural frequency the structure will experience maximum vibration velocities and maximum displacement amplitudes The condition where the natural frequency and the driving frequency are equal is called resonance Any motion that repeats itself is called periodic or harmonic motion Simple harmonic motion is a sinusoidal inction in time In simple harmonic motion acceleration is directly proportional to displacement but opposite in sign Acceleration and displacement are related by the square of the frequency If a spring follows Hooke s law a mass bouncing off of a massless spring exhibits simple harmonic motion In simple harmonic motion there is an oscillation between kinetic and potential energy with no energy being lost to the surroundings Period for motion of a mass on a spring 0 T 2pi square root mk Period is inversely proportional to velocity A pendulum has total gravitational energy at the top of its swing and total kinetic energy at the bottom 0 T 2pi square root Lg Unexpected examples of simple harmonic motion 0 Orbit of a planet viewed from the side 0 Tether ball game viewed from the side 0 Electrons oscillating back and forth in AC current The Doppler effect results because waves are unaffected by the speed of the source which produces them 0 This causes an observer not to hear sound with the pitch with which it was emitted and also causes an observer not to see light with the color with which it was emitted Approximation of Doppler effect 0 Change in frequencysource frequency vc 0 Change in wavelengthsource wavelength v c When relative velocity brings source and observer closer the observed frequency goes up and observed wavelength goes down The relative velocity is the net speed at which the source and observer are approaching each other For light when the source and observer are approaching each other the wavelength shortens creating a blue shift When they separate the wavelengths lengthen creating a red shift For objects moving in same direction at same speed there is no Doppler effect The relative velocity is zero and therefore the frequency is zero Current runs in the opposite direction of electrons The net charge in the universe and net charge is created by separating electrons from protons Charge on proton and electron l6xl0quotl6C Coulomb s law 0 F kqqrquot2 0 K 899xl0quot9 A major difference between gravitational and electric forces is that gravitational forces are always attractive and electric forces may be attractive or repulsive The center of charge exists at the center of a hollow sphere even though there is no actual charge at this center Lines of electric force point from positive to negative Electric eld E kqr 2 Force on a charge in an electric eld o F Eq Potential energy of a charge in an electric eld o U Eqd Electric potential is zero for particles separated by an in nite distance Voltage Ed which is the potential for work by an electric eld in moving any charge from one point to another Voltage due to a point charge kqr Within an electric eld movement perpendicular to the eld does not result in change in potential P qd which is an electric dipole which is created by two charges with the same magnitude but moving in opposite directionsTHIS DIPOLE POINTS FROM NEGATIVE TO POSITIVE WHICH IS OPPOSITE IN CHEMISTRY At large distances the electric eld of a dipole varies by lrquot3 A dipole placed in an electric eld will tend to align itself in orientation opposite that of the eld A dipole not perfectly aligned will have potential energy of U pEcostheta Voltage workcharge Poor conductors are represented by network solids such as diamonds and glass The electric eld inside a uniformly charged conductor is 0 Current moving charge which is measured in amps or Coulombssecond The direction which the positive charge moves Just like uids electrons move in all random directions but at a slower speed they move in a single direction called drift speed Rho stands for resistivity here just as it has stood for density previously Resistance resistivitylengtharea o If a length of wire is doubled or crosssectional area cut in half the resistance is doubled Voltage currentresistance A node is any intersection of wires Kirchhoff s first rule the amount of electricity owing through a node is the same that goes into the wire Kirchhoff s second rule the voltage around a circuit must sum to 0think of this as the displacement vector if you end up back where you started then the displacement is zero Battery adds energy to a circuit by increasing voltage between one point and the other Assume batteries have no internal resistance unless otherwise indicated Capacitor used to temporarily store energy in a circuit In a parallel plate capacitor two plates are placed parallel from one another One is positively charged and one is negatively charged They both hold the same exact amount of charge and there is a uniform electric eld throughout the capacitor K l4piepsilon Electric eld lKQAepsilon 0 K dielectric constant 0 Q charge on either plate 0 A area Something with high capacitance can store more charge at a lower voltage C QV Charge sits on the surface of a charged conductor not within it o For this reason an increase in the thickness of the plates of a capacitator do not increase how much charge is held by them The farther the plates are separated the greater the voltage the lower the capacitance C K Aepsilond 0 K dielectric Area under a chargevsvoltage graph is the energy U 12QV o This equation represents the potential energy sustained by a capacitor The dielectric constant refers to the substance between the plates of the capacitor which must be an insulatorotherwise it would conduct charge and not allow buildup of charge 0 Dielectric acts to build up electric eld and thus allow greater capacitance 0 Also acts to limit the amount of voltage across the plates 0 Work is done on the dielectric to induce its dipoles to point towards the electric eld and then this energy is stored Dielectric of Air is close to one and in a vacuum is 0 unity ALL OTHERS INCREASE FROM THERE Lines connecting components of a circuit are completely nonresistive wires When resistors are in series their total effective resistance is the sum of all of their individual resistances When resistors are in parallel their total effective resistance RECIPROCAL is the sum of all of their individual reciprocals WITH CAPACITORS THE OPPOSITE RELATIONSHIP IS TRUE Power IV 0 Iquot2RVquot2R BUT THESE 2 EQUATIONS ARE ONLY APPLICABLE TO energy dissipated as heat BY A RESISTOR The current going through a resistor generates heat The rate at which heat is generated is power dissipated The electric eld is constant throughout a capacitor and the dipoles on either end point in opposite directions Thus the net force 0 Adding a resistor in parallel decreases overall resistance The voltage of the battery is not affected by changes within the circuit Direct current is when the electrons move in a single direction around the circuit Alternating current is generated by movement of electrons in simple harmonic motion 0 Voltage or current in alternating current is described by a sine inction Maximum voltage square root2Vrms 0 V voltage 0 You may use the same equation but replacing the Voltages with Currents 0 Note the Vrms is NOT under the square root Magnetic eld and radius are related by the BioSavart Law 0 B mui2pir Rms voltage in US is typically 120 V with maximum voltage being l70V Magnetic eld is measured in units of T or Tesla Magnetic poles have never been found to exist separately one pole always accompanies the other Magnetic lines point from the north pole to the south pole A changing electric eld becomes a magnetic eld A stationary eld does not create a magnetic eld Magnetic elds follow the inverse square law when it comes to distance Direction of magnetic eld due to a currentcarrying wire 0 Use right hand rule 0 Grab wire with nger pointing in direction of the current 0 The direction in which ngers point is the direction of the magnetic current F qvBsintheta o Theta is the angle between the magnetic eld and the velocity of charge Force is directed perpendicularly to magnetic eld amp velocity Second right hand rule is used to nd direction of force 0 Thumb remains pointing in direction of current of a positive charge 0 Fingers point in direction of magnetic eld o The palm of one s hand points in the direction of the force 0 if the charge is negative the palm rule is reversed and the back of the hand is what points in direction of force Since electric force is always perpendicular to velocity it does no work Force changes direction but never the magnitude of velocity Force always acts as centripetal force and can be set equal to mvquot2r in order to nd radius of curvature of the particle F iLBsintheta A changing magnetic eld creates an electric eld which is NOT conservative and is instead dissipated as heat in the charged particle Forces due to an induced electric eld are not conserved F qvB X s mean magnetic eld is directed INTO the page Circles mean the magnetic eld is directed out of the page A charged particle moving parallel to a magnetic eld experiences no force A current will ow in a loop of wire to oppose changes in magnetic eld inside the loop A changing electric eld creates a magnetic eld and the converse is also true An electromagnetic eld is a transverse oscillation where the two elds electric and magnetic are perpendicular to each other and the direction of propagation is similarly perpendicular to both 0 All are created by acceleration of electric charge Speed of propagation of electromagnetic eld EB Rate at which an electromagnetic wave is transferring energy per unit area 0 EBsintheta poynting vector Visible light spectrum 390 10 9 to 700 10 9 o Shorter wavelengths correspond to violet light and longer wavelengths correspond to red light o Wavelengths towards the violet part of the spectrum have more energy remember this by knowing that they have so much energy that ultraviolet light which is just beyond visible violet light has so much energy that it gives you sunbum Index of refraction speed of light propagating through a medium 0 Ncv I C speed of light through a vacuum The greater the index of refraction the slower the light moves through that medium Ray will tum towards normal as it enters the glass and away from normal as it exits the glass Re ection is indicative of either wave or particle theory diffraction occurs when waves bends around comers Water n 13 Glass n 15 Each photon in light represents an electromagnetic wave Isotropic light light emanating from a point source Planepolarized light light with electric elds all pointing in one orientation When isotropic light is polarized it loses one half its density as it loses light in one direction and keeps all light perpendicular to that direction Angles of re ection and refraction are measured from a line normal to the medium Angle of re ection angle of incidence Collision of photon against a medium is completely elastic and they lose no kinetic energy Snell s law 0 Nlsinthetal n2sintheta2 The path that light travels is the one which would take the shortest time When light crosses into a new medium the frequency stays the same but the wavelength changes Energy of light hf 0 Thus higher frequencies lower wavelengths have higher energies o This equation gives energyphoton o If we double the frequency we double the photons and we increase intensity by a factor of 4 When light is coming from a medium with a higher incidence of refraction the angle of incidence could be so great so as to cause total intemal re ection Critical angle theta inverse sinn2nl Longer wavelengths move faster through a medium than shorter wavelengths and therefore bend less dramatically Chromatic dispersion the spreading of light by a prism spreads white light into all colors of the visible spectrum All types of waves refract and diffract Diffraction 0 When a wave moves through an aperture it bends around the comer of the opening 0 Only signi cant when aperture size is on the order of the wavelength or smaller 0 The smaller the aperture and the longer the wavelength the greater the diffraction 0 When waves diffract constructive light bands interference and destructive dark bands interference occur 0 May also result in dispersion or creation of colors Mirrors re ect light lenses refract light Re ection in a at mirror is a virtual image Diverging lenses are concave Converging lenses are convex Thicker center in a lens converges light Smaller radius of curvature indicates a sharper tum Light is re ected by concave mirrors and refracted by converging lenses through a focal point Light is re ected by convex mirrors and refracted by diverging lenses away from a focal point Focal length of a mirror M2 Factors affecting focal point of a lens 0 Radius of curvature 0 Index of refraction of lens and of medium When nln2 a lens will not refract light Focal point of a lens varies with frequency resulting in chromatic aberration Power of lens inverse of focal length lf Lenses are considered in nitely thin so refraction occurs at the center of the lens Lateral magni cation 0 Height I height o dido If this quantity comes out to be negative the image is inverted Thin lens equation 0 lf ldo 1di I eye is positive that real is inverted System for determining lensmirror problems 0 First draw an eye on one side of the paper This is the observer On the side with the eye write real positive inverted Images and focal points on the opposite side will be virtual negative and upright In dealing with a mirror the eye is in front of it just as you stand in front of a mirror In dealing with a lens the eye is behind it just as you stand behind a camera lens to take a picture Objects are always positive when they are in front of a lens or a mirror and they are always negative when they are behind a lens or a mirror If object is in front convex mirrors and diverging lenses make negative virtual and upright images F IS ALWAYS NEGATIVE o Concave mirrors and converging lenses make positive real and inverted images except when the object is WITHIN the focal distance THEN the image is negative virtual and upright F IS ALWAYS POSITIVE o BOTH THE ABOVE RULES ONLY APPLY WHEN THE OBJECT IS IN FRONT IF OBJECT IS BEHIND REVERSE THEM IN TWOLENS SYSTEMS BE CAREFUL AS THE OBJECT OF THE SECOND LENS WHICH IS THE IMAGE OF THE FIRST LENS MAY BE BEHIND THE SECOND LENS M l1dof Ml di f In a singlelens system the object cannot be behind the mirrorlens nor can it have a negative distance Two lens system 0 Lateral magni cation of system mlm2 0 Power of system plp2 Positive magni cation gives a virtual upright image and negative magni cation gives a real inverted image Diverging lens and convex mirror only produce images smaller than the object Converging lenses and concave mirrors produce images smaller than object when object is more than 2 focal lengths away from mirror 0 Image is larger when object is within 2 focal lengths o O OOOOO
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