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AS Level Physics for OCR AG481 - Mechanics; G482 - Electrons,Waves and Photons

ContentsArticles

A- level Physics 1

Module 2821 - Forces and Motion (matched to new module G481 -Mechanics) 3

A- level Physics/ Forces and Motion/ Scalars and vectors 3A- level Physics/ Forces and Motion/ Dynamics 6A- level Physics/ Forces and Motion/ Force, work and power 8A- level Physics/ Forces and Motion/ Deformation of solids 10

Module 2822 & 2823 - Electrons and Photons; Wave Properties (matchedto new module G482 - Electrons, Waves and Photons) 12

A- level Physics/ Electrons and Photons/ Electric current 12A- level Physics/ Electrons and Photons/ D. C. circuits 16A- level Physics/ Electrons and Photons/ Quantum physics 18A- level Physics/ Electrons and Photons/ Electromagnetic waves 20A- level Physics/ Wave properties/ Reflection and Refraction 22A- level Physics/ Wave properties/ Waves 23A- level Physics/ Wave properties/ Superposition 24

Appendices 25

A- level Physics/ The SI System of Units 25A- level Physics/ Symbols for Physical Quantities 28A- level Physics/ Equation Sheet 30A- level Physics/ Glossary of Terms 31A- level Physics/ Forces and Motion/ Kinematics 34

ReferencesArticle Sources and Contributors 40Image Sources, Licenses and Contributors 41

Article LicensesLicense 42

A-level Physics 1

A- level PhysicsThis A-level physics book is designed to follow the OCR GCE Physics A specification [1]. For the OCR B'Advancing Physics' specification, see A-level Physics (Advancing Physics). You can use this book as a revisionguide, or as another explanation of concepts that you may not fully understand. At A2 level, in the second year ofstudy, you must take the two core A2 modules along with one of the option modules.Before you begin this course, it is recommended that you understand some of the basic concepts covered in GCSEScience, and have an understanding of the SI unit system (Appendix A).If you find any mistakes, errors, broken links, or if you are able to make the content easier to understand, please donot hesitate to edit and expand on existing content.

Modules

AS Modules• Force(s) and Motion• /Electrons and Photons/• /Wave Properties/• /Electricity/A2 Core Modules

• /Forces, Fields and Energy/• /Unifying Concepts in Physics/A2 Option Modules

• /Cosmology/• /Health Physics/• /Materials/• /Nuclear and Particle Physics/• /Telecommunications/

AppendicesAppendix A

• /The SI System of Units/Appendix B

• /Symbols for Physical Quantities/Appendix C

• /Equation Sheet/Appendix D

• /Glossary of Terms/

A-level Physics 2

References[1] http:/ / www. ocr. org. uk/ qualifications/ asa_levelgceforfirstteachingin2008/ physics_a/

3

Module 2821 - Forces and Motion (matchedto new module G481 - Mechanics)

A- level Physics/ Forces and Motion/ Scalars andvectorsVectors and scalars are mathematical constructs which physicists employ. Some physical quantities are representedby scalars and some by vectors and corresponding operations are employed upon them while dealing with them.Vector quantities have a direction associated with them while scalars are treated like simple numbers. The followingare some examples of quantities that are represented as scalars and vectors.

ScalarsThe following quantities have a magnitude but no direction associated with them, and are examples of scalars:• distance• speed• time• mass• energy• density

Addition of scalarsAdding scalars is simple, all you need to do is add the numbers together. For example, 5m + 3m = 8m, or 76b + 23b= 99b

Multiplication and division of scalarsMultiplying and dividing scalars is the same as multiplying and dividing normal numbers.You should also remember to multiply and divide the units, so that you can check your answers are given in thecorrect units. For example, if you were finding the area of a surface: . The unit of area is ,so this is correct.

VectorsThe concept of direction establishes a relationship between two points in space; that is, the "direction" from onepoint to another. For example, the direction from point A to point B could be designated A-to-B while the oppositedirection would be in that case B-to-A. Direction is dimensionless; that is, it has no measurement units andrepresents only a line designating the sense of from-to (from A to B) with no sense of "how much" which isconsidered the "magnitude" of a measurable quantity."Magnitude" provides a sense of "how much" (or "how many") of a measurable quantity. The term five miles has amagnitude of five units of measure; this unit of measure is miles.When magnitude ("five" miles) is coupled with direction (let's say north; which is the dimensionless direction from me to the North Star) we obtain "five miles north"; this is a "vector". A "vector" has both magnitude and direction. A

A-level Physics/Forces and Motion/Scalars and vectors 4

special type of vector has a magnitude of one in a given direction and is called a “unit vector” for that direction. Aquantity that has only magnitude but has no associated direction is a "scalar", as described earlier.Two vectors that have the same direction and magnitude are equal; a vector from me that is "five miles north" isequal to a vector from you that is "five miles north"; wherever you are. However, the position obtained by movingfrom me to "five miles north" of me is not a vector. The vector is the "displacement" that consists of a magnitude ofdistance (five miles) and a direction (north). A position can be represented by a beginning reference point (you;wherever you are) and a vector (five miles north), but a vector alone is not a location; it must have a referencelocation to be meaningful as a position.The following quantities have both a magnitude and a direction associated with them, and therefore are vectors:• Displacement (e.g., five miles north)• Velocity (50 metres per second, bearing 60 degrees 15 seconds)• Acceleration (32 feet per second per second straight up)• Weight (your weight straight down)• Force (the amount of energy in a given direction)Vectors can be represented in any set of spatial dimensions, though typically they are expressed in 2-D or 3-D space.

MultiplicationWhen you multiply a vector by a scalar, the result is a vector. Its direction is unchanged if multiplied by a positivescalar and its direction is reversed when multiplied by a negative scalar. The vector's magnitude is simply multipliedby the scalar.There are two different kinds of multiplication when you multiply two vectors together. There is the dot product, andthere is the cross product. The multiplication of two vectors is outside of the scope of an A-level physics course, butyou can find out about them on Wikipedia.

Addition of vectorsVectors can be added like scalars as long as they are facing the exact same direction. If the vectors are in oppositedirections, you must subtract one from the other, and unless stated otherwise, you should use the commonconventions that:• up is positive, and down is negative, and• right is positive and left is negative.When the vectors aren't in a straight line, you must use another method to find their sum.

Pythagoras' theorem

If the two vectors are perpendicular to each other, it is possible tofind the total vector using Pythagoras's theorem, with the resultantvector being the hypotenuse of the right-angled triangle.

The direction of the resultant can be found using the formula: , where is one of the sides touching

(adjacent to) the angle, is the side opposite the angle, and is the angle of the resultant vector.

A-level Physics/Forces and Motion/Scalars and vectors 5

Notice that vector a has no effect in the direction of vector b, and similarly, vector b has no effect in the direction ofvector a. When two vectors are perpendicular to each other, it is said that they act independently of each other.

Resolving vectors into two perpendicular components

A vector can be broken down into components, which areperpendicular to each other, so that the vector sum of these twocomponents, is equal to the original vector. (Usually, it isinteresting to break down a vector into two perpendicularcomponents, such that one is vertical and the other horizontal.However, the components do not have to be chosen to be verticaland horizontal always; they only need to be perpendicular to eachother). Splitting a vector into two components is called resolvingthe vector. It is the reverse of using Pythagoras' theorem to addtwo perpendicular vectors, and so adding the two components willgive you the original vector. There are many uses for vectors thathave been split in this way.

Resolving a vector requires some simple trigonometry. In the diagram, the vector to be resolved is the force, . Forangle :• the horizontal component of : , and• the vertical component of : .Note that the two components do not have to be horizontal and vertical. The angle can be changed to anyrequired direction, and both components will still be perpendicular to each other.

A-level Physics/Forces and Motion/Dynamics 6

A- level Physics/ Forces and Motion/ DynamicsDynamics is the study of why objects move, and the effects of forces on moving objects.

MassWhen you are standing on a bus, and the bus starts very quickly, your body seems to be pushed backward, and if thebus stops suddenly, then your body seems to be pushed forwards. Notice that when the bus turns left, you will seemto be pushed to the right, and when the bus turns right, you will seem to be pushed to the left.Also consider a full shopping cart. If you try to push it from a stationary position, it will take some effort to get itmoving. The same is true if you try to stop it when it is moving at a high speed, or try to turn it left or right.In both cases, an object with mass is opposing a change in motion. In the first case, it is your body that tries to staymoving as it was before the change. Your body also tries to stay in a straight line when the bus turns, although itappears to be moving to the side. What is really happening is that your body is still moving straight and the bus turnsin the opposite direction. The shopping cart exhibits the same behaiviour. When it is stationary, it tries to staystationary, and when you try to stop it moving, it will try to continue. Your body and the cart both have mass.From this, we can define a property of mass:

Mass will resist changes in motion.This says that any object with mass will resist any change in motion. Objects with greater mass will resist change inmotion more than objects with less mass. It is like having the shopping cart only half full and finding that it is mucheasier to change its movement. This is Newton's first law of motion: An object at rest will remain at rest unless actedupon by an outside force. Conversely: An object in motion will remain in motion unless acted upon by an outsideforce.In the SI system, the unit of mass is the kilogram (kg).

ForceWe all have an innate understanding of forces. To put quite simply, a force involves a push or a pull. Exerting a forceon an object will cause that object to accelerate.Try pushing your finger against a wall. By doing this, you are said to exert a force on the wall. You will feel the wall'pushing' back on you. The wall is said to exert a force on you. The force you exert on the wall always equals theforce with which the wall exerts on you (Newton's Third Law).* Note that the forces are acting on different bodies.Because the wall is heavy, the force you exert on it does not move the wall noticeably. However, being much lighter,you will be probably be moved by the force that the wall exerts on you. Try it!A force can be applied to an object in different directions. Force is said to be a vector quantity.

Force and AccelerationExerting a force on an object causes the object to accelerate. The same force applied on objects of different massescauses different accelerations in each object. We observe that a force applied on a light object causes greateracceleration than the same force applied on a heavier object. We also observe that the acceleration of an object isproportional to the force exerted on it.This is summarized by the formula F = kma, where F=force, k=some constant, m=mass and a=acceleration.

A-level Physics/Forces and Motion/Dynamics 7

Defining the NewtonIn the SI unit system, force is measured in Newtons. One Newton is the force required to accelerate a mass of 1 kg at

. Therefore, we have defined the unit of force in such a way that the value of k in F = kma is 1, therebyreducing the equation to F = ma.1 N = 100000 dynes = 0.101971621298 kgforce = 0.2248089431 lbforce1 dyne = 1E-5 Newtons, 1 kgforce=9.80665 Newtons, and 1 lbforce=4.44822161526 Newtons

WeightThe weight of an object is defined as the gravitational force acting on the object, and is dependent on the mass of thebody. Note that the acceleration due to gravity (or acceleration of free-fall, usually denoted by g) is taken as theconstant for all bodies, although it varies slightly from place to place. The direction of that force(weight) is always toward the center of this planet. We can calculate the weight of an object from its mass by theequation W = mg, where W=weight, m=mass and g=acceleration of free fall. In rough terms, an apple weighsapproximately one Newton.• Newton's third law: For every action, there is an equal and opposite reaction.

Motion of particles through fluidsMechanics of particle motion.There are three forces acting on particles in motion through a fluid;1) The external force (gravitational or otherwise);2) The drag force (apparent when there is relative motion between a particle and a fluid);3) The buoyant force (acting parallel to the external force, but in the opposite direction).

Density

ViscosityViscosity of a fluid is a measure of its resistance to flow. Objects drag fluid along near its surface. The faster theobject moves, the bigger the viscous drag.

A-level Physics/Forces and Motion/Force, work and power 8

A- level Physics/ Forces and Motion/ Force, workand power

WorkWork is a special name given to the (scalar) quantity

where is work and is force on the object and is displacement. Essentially this integral is the component ofthe force in question in the direction of the displacement, times the displacement. If the force is constant and theobject travels in a straight line, this reduces to

where is work and is force on the object and is displacement. Take note of the dot product.We say that W is the "work done by the force, F." Notice that need not be the total force on an object, just theforce we are looking at. It makes sense to ask what is the work done by a given force on an object. Notice also thatthe work done by the sum of two forces acting on an object is the sum of the work done by the forces actingindividually on the object. This gives rise to the interpretation that work is that it is the energy transferred to the bodyby a force that acts on it. (Of course negative work is energy transferred from the body). This is the whole point ofeven considering work.

For, say we had a total force acting on an object. Then the work is

This simply uses Newton's second law in the first step and a substitution in the integral. This states that the workdone by the total force on an object is the change in kinetic energy of the object. For example, if you hold an apple,then move the apple down a little bit then stop, what is happening? Surely the potential energy of the apple haschanged, so someone is doing work even though there is no change in kinetic energy -- how can that be? We mustconsider all the forces. Gravity did work on the apple, but the apple did work on you (you did negative work on theapple) -- you have absorbed the energy! So there really is no paradox after all.In a very special case, it happens that the the quantity of work does not depend on how you move a particle around,but only on the beginning and ending points. Such a field is called "conservative." It means that we can introduce apotential. Gravity is such a conservative force, amazingly, which is why we can talk about the "potential energy" ofan object. It is just shorthand for saying the work it takes to move the object from somewhere (the reference point) towherever we are talking about. Consequently, the change in kinetic energy equals the negative change in potentialenergy, which basically states that the total energy of the system is constant. This is in fact why such a force is calledconservative -- it conserves mechanical energy!Dissipative forces, such as friction (it always eats up energy) are sometimes called non-conservative forces. This issomewhat of a mistake because on the molecular level, the forces really are conservative. However, it is often nicerto just say that energy is not conserved in a given scenario, even though we know full well that it is disappearing intothe motion of atoms, or heat. You will hear many people say that energy is not conserved in a given situation, but ofcourse it is; energy is always conserved.It turns out that a force is conservative if and only if the force is "irrotational," or "curl-less" which has to do withvector calculus. But for all of our purposes, there are no non-conservative forces!However, just to quantify everything, we have the work done by a non conservative force is the change in the totalenergy of the body.

A-level Physics/Forces and Motion/Force, work and power 9

PowerPower is the rate of doing work. Thus we have

So,

,

and for forces that do not vary over time becomes

.

This means that if the force is acting perpendicular to the velocity, the speed does not change, because the work iszero so the change in kinetic energy is zero. But wait, how can that be, since a force necessarily acceleratessomething? It is accelerating it, it is changing the direction of travel -- acceleration means the derivative of the vectorvelocity, not the magnitude of velocity. In fact, this tells us that the component of force in the same direction asvelocity is responsible for (and only for) changes in the magnitude of the velocity, and the component of forceperpendicular to the velocity is responsible for (and only for) changes in the direction of the velocity. Just to quantifythis a little bit, it can be shown that

where a is acceleration, v is the velocity, T is the unit tangent vector (tangent to the path of the particle andconsequently parallel to the velocity vector), N is the unit normal vector (perpendicular to the tangent vector and inthe direction of the derivative of the tangent vector, which you can picture by drawing two pretty close tangentvectors on a curve), and is the radius of curvature, which is essentially the radius of the circle which closest fitsthe path at the point (the radius of curvature of a circle is the radius of the circle, and the radius of curvature of astraight line is infinity). All this business is not really necessary for understanding physics, but if you understand it itwill help you understand what is going on. Notice that the second term is the centripetal acceleration -- this is in factwhere we get the formula for it.Finally, just writing out the definition of power to look pretty, if the work is done at a changing rate, then

If the work is done at a constant rate, then this becomes

.

A-level Physics/Forces and Motion/Force, work and power 10

PressurePressure is the force per unit area.

Torque

Torque is the "rotational force" applied as part of circular motion, such as the force making the wheels of a car turn.In the SI unit system, torque is measured in Newton-metres.

A- level Physics/ Forces and Motion/ Deformationof solids

Hooke's law

This applies to an objects deformation only before the elastic limit; from then on it deforms plastically and no longerfollows this law.

Spring Constant

The gradient refers to the gradient of a Tension-Extension graph.The standard units of k are N m-1

Strain

Because this is a division of two measurements of length, Strain has no units and remains a ratio.

Stress

The units for Stress are N m-2, otherwise known as Pascals (Pa)

A-level Physics/Forces and Motion/Deformation of solids 11

The Young's modulus

Strain energy

However, due to Hooke's Law, it can be calculated in another form;

12

Module 2822 & 2823 - Electrons andPhotons; Wave Properties (matched to new

module G482 - Electrons, Waves andPhotons)

A- level Physics/ Electrons and Photons/ ElectriccurrentElectricity is useful because we can easily transform electrical energy to other forms of energy such as light, soundand heat. Electricity is transferred from place to place by wires as an electric current.

Current and ChargeElectric current is the flow of charged particles, usually electrons, around a circuit. Metals are good conductors ofelectricity because they have free electrons that can move around easily.Current is measured in amperes, or amps.Charged particles have a charge which is either positive or negative. The strength of a charge can be found using theformula:

where Q is the quantity of charge in coulombs, I is the current in amps, and t is the time in secondsWe can use this formula to define the coulomb:

One coulomb is the amount of charge which flows past a point when a current of 1 ampere flows for 1 second

Electron flowWhen you attach a battery to a small bulb with wires, you would say that the current is flowing from the positiveterminal of the battery to the negative one. This is called conventional current. The electrons, however, flow fromthe negative terminal to the positive. This electron flow is in the opposite direction to the conventional current, andcare must be taken to not confuse the two. When we just say current it is assumed that we are talking aboutconventional current.The reason for this is that the direction of conventional current was chosen before people knew what was happeninginside a conductor when a current flows.

A-level Physics/Electrons and Photons/Electric current 13

ResistanceAny component with electrical resistance opposes the flow of an electrical current.

Electrical ResistanceIn an electrical circuit, current flows around it. Each component in the circuit has a resistance, which resists the flowof the current.The voltage that you get from the power supply can be simply described as the "push" given to the electrons to goaround the circuit.It would then make sense to say that the greater the voltage, the greater the current, and the greater the resistance, thelower the current. The current flowing around the circuit could then be written as the equation:

.

For example, if you were to connect a 9 volt power supply to a 3 Ω (read as 3 ohm) resistor, you could use theformula above to find the current. , so .

A particular arrangement of this formula is used to define resistance and the ohm.

.

This says that the resistance of a component is the voltage across it for every unit of current flowing through it. Moreformally this can be written as:

The resistance of a component in a circuit is the ratio of the voltage across that component to the current in it.The unit of resistance, the ohm (Ω), is defined so that one ohm is the resistance of a component that has a voltage of1 volt across it for every amp of current flowing through it. In other words, one ohm is one volt per amp.

Ohm's LawIn many components, the voltage across it is proportional to the current flowing through it. You can make thisobservation on a circuit with a resistor of a known resistance, a voltmeter, an ammeter, and a power supply with avariable voltage. As you increase the voltage, the current will also increase. You will come to the conclusion that

, with the constant of proportionality equal to . This gives us , an arrangement of thefamiliar formula.Components where , are known as ohmic conductors, and have a constant resistance. They are said tofollow Ohm's law, which states that:

For a conductor at constant temperature, the current in the conductor is proportional to the voltage across it.

OR

with all physical conditions (such as temperature,dimensions of the conductor) remaining constant,the currentflowing through the conductor is directly proportional

Note that not all components are ohmic conductors, and can have varying values of resistance. You will have to usethe formula to find the resistance for specific values of and .

Below you can see 3 graphs with current on the vertical axis, and voltage on the horizontal axis. Where the graph is astraight line, the voltage is proportional to the current. Therefore, only the metallic conductor is an ohmic conductor.

A-level Physics/Electrons and Photons/Electric current 14

A diode and a filament lamp are two examples of non-ohmic conductors. The diode is designed to only allowcurrent through in one direction, hence the use of negative values on its graph. The filament lamp doesn't have aconstant temperature, which according to Ohm's law is required for a component to be an ohmic conductor. Instead,it heats up as a current passes through it, which has an effect on the resistance.

ResistivityThe resistivity of a material is the property that determines its resistance for a unit length and unit cross sectionalarea of that material. Copper, for example, is a better conductor than lead, in other words lead has a higher resistivitythan copper. You can compare different materials in this way.Resistivity, ρ (the Greek letter rho), is defined by the equation:

Where ρ is resistivity, R is the resistance, A is the cross sectional area of the material, and l is the length of thematerial.The units of resistivity are Ohm-meters, Ωm.If we rearrange the above equation so that:

You can see that as the length of a wire is increased, its resistance will increase, and as the cross sectional area of awire is increased, its resistance will decrease. This is true provided that the temperature is constant, and that the samematerials are always used, to make sure that the resistivity stays the same.

Voltage and EnergyEarlier, we simply said that a voltage is the "push" given to electrons, or units of charge. Now, we will take a look atvoltage in terms of energy, and find a more accurate definition of the volt.

Potential DifferenceWhen you attach a voltmeter across a component, the voltage you are measuring is a potential difference (PD).Electrical energy is being used up by the component, and so we can say that a potential difference is a voltage wherethe charge is losing energy. Potential difference has the symbol V.Potential difference is the energy lost per unit charge, and can be written as the following formula:

A-level Physics/Electrons and Photons/Electric current 15

Electromotive ForceA battery provides a certain voltage to the circuit, and the electrons are gaining energy from the battery as they flowpast. This voltage where the charge gains energy is called an electromotive force (EMF), and has the symbol V.EMF. is the energy gained per unit charge, and can be written as the following formula:

Both the PD and EMF are measured in volts, and one volt is equivalent to one joule per coulomb.

Electrical Energy and PowerPower is the rate at which energy is transferred, written as the formula:

To find a formula for electrical power, we take the following formula for voltage and make W the subject:

Then we need to divide both sides by t to get power:

Recall that charge divided by time is current, we now have:

From the formula above, you can see that the electrical power is simply the product of current and voltage. You cancombine this with to give two further equations:

One last formula is for energy and is derived from the formula for power:

A-level Physics/Electrons and Photons/D.C. circuits 16

A- level Physics/ Electrons and Photons/ D. C.circuitsA direct current (DC) circuit usually has a steady and constant voltage supplied to it. A direct current does not have acontinually changing polarity, unlike an alternating current (AC), but instead a constant direction and rate of flow.DC is generally provided by batteries or via a transformer, rather than generators.

Circuit diagramsBelow are the symbols and names for all of the components that you are required to know:

Series circuitsWhen resistors are set up in series, the formula to work out the total resistance is:

Where etc., are the resistance of each resistor in series.

Parallel circuitsWhen resistors are set up in parallel, the formula to work out the total resistance is:

Where etc., are the resistance of each resistor in parallel.

A-level Physics/Electrons and Photons/D.C. circuits 17

Internal resistanceA electrical source has its own resistance, known as Internal Resistance. This is caused by the electrons in thesource having to flow through wires within it, or in the case of a chemical battery, the charge may have to flowthrough the electrolytes and electrodes that make up the cell.By considering a battery of EMF E, in series with a resistor of resistance R we can calculate the internal resistance r:

(See Series Circuits above)Combining with V=IR:

The quantity Ir is called the lost volts. The lost volts shows us the energy transferred to the internal resistance of thesource, so if you short circuit a battery, I is very high and the battery gets warm.

Potential dividersA potential (or voltage) divider is made up of two resistors. The output voltage from a potential divider will be aproportion of the input voltage and is determined by the resistor values.The values of a battery with voltage V1 passing through two resistors in series of resistance R1 and R2, with anoutput circuit in parallel with Resistor R1 with output voltage V2 are related by the equation:

Kirchhoff's lawsFirst Law states "The sum of the current (A) entering a junction is equal to the sum of the current (A) leaving thejunction". This is a consequence of conservation of charge.Second law states that the EMF is equal to the voltage of the circuit. This is a consequence of conservation ofenergy.

Use of other componentsThermistors can be placed in circuits when temperature plays a role. As the temperature increases, the resistance ofthe device decreases. This does not obey the Ohms law. Light dependent resistors are resistors that decrease theirresistance when exposed to light.

A-level Physics/Electrons and Photons/Quantum physics 18

A- level Physics/ Electrons and Photons/Quantum physicsQuantum physics tries to explain the properties of matter and energy at the atomic and subatomic levels. We usequantum physics to model behaviour and properties of microscopic objects that cannot be modelled by Einsteinianphysics, which is the physics used for objects at the macroscopic level (as viewed with the naked eye).

Does light behave as a wave or as particles?Interference experiments, such as Young's Slits (see below) can only be explained if we assume light is a wave.However, the photoelectric effect can only be explained if light is a particle. So what is light - particle or wave?The best thing to remember is that both waves and particles are nothing more than physical models for explainingour observations. For example, someone might think of counting apples when they are learning basic arithmetic; thisdoes not mean that numbers are apples, only that we can think of them as such in certain specific circumstances.When we get to the concept of negative numbers, using apples as a model breaks down unsurprisingly. Similarly, inquantum physics, we find that we must use different models for different situations.

Young's SlitsThomas Young conducted a famous experiment in which light was diffracted by a double slit and produced aninterference pattern on a screen. An interference pattern is a pattern of bright and dark bands caused by theconstructive and destructive interference of the rays from the two slits, and is only a feature of waves. Electrons areusually considered to be particles, but produce apparent interference patterns by diffracting. To produce aninterference pattern, you must have a wavelength. This gives more evidence of Wave-particle duality.

The Photoelectric EffectIn analysing the photoelectric effect quantitatively using Einstein's method, the following equivalent equations areused:Energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electronAlgebraically:

where• h is Planck's constant,• f is the frequency of the incident photon,• is the work function, or minimum energy required to remove an electron from atomic binding,

• f0 is the threshold frequency for the photoelectric effect to occur,

• is the maximum kinetic energy of ejected electrons,

• m is the rest mass of the ejected electron, and• is the velocity of the ejected electron.

Note: If the photon's energy (hf) is less than the work function ( ), no electron will be emitted. The work functionis sometimes denoted .

A-level Physics/Electrons and Photons/Quantum physics 19

Planck constantThe physicist Max Planck studied a phenomenon known as black-body radiation, and found that the transmission oflight was best treated as packets of energy called photons. The energy of a photon, , is given by the followingformula:

where is the energy of the photon, is the Planck constant, , and is the frequency of thelight. Since the velocity of light (which is c in a vacuum) is given by , it may be helpful to use the equation

if you are given the wavelength of light and not the frequency.

The Photon ModelOver the ages, scientists have argued what light actually is. Newton argued that light is composed of particles calledcorpuscles and theorised that diffraction was due to the particles speeding up as they entered a denser medium, beingattracted by gravity. However he has since been proved wrong, now we can measure the speed of light and haveproved it to slow down in a denser medium. Albert Einstein thought that light were discrete packets of energy whichhe called quanta.

Wave-particle dualityIn 1924, Louis-Victor de Broglie formulated the de Broglie hypothesis, claiming that all matter has a wave-likenature; he related wavelength, λ (lambda), and momentum, p:

This is a generalization of Einstein's equation above since the momentum of a photon is given by p = E / c where c isthe speed of light in a vacuum, and λ = c / ν.De Broglie's formula was confirmed three years later for electrons (which have a rest-mass) with the observation ofelectron diffraction in two independent experiments. At the University of Aberdeen, George Paget Thomson passed abeam of electrons through a thin metal film and observed the predicted interference patterns. At Bell Labs ClintonJoseph Davisson and Lester Halbert Germer guided their beam through a crystalline grid.

A-level Physics/Electrons and Photons/Electromagnetic waves 20

A- level Physics/ Electrons and Photons/Electromagnetic waves

StructureElectromagnetic (EM) waves are transverse waves that carry energy. This means the light can be polarised like allother transverse waves. Depending on the amount of energy, the waves create the electromagnetic spectrum,comprising (from longest to shortest wavelengths) radio, microwave, infra-red, visible light, ultraviolet, X-ray,gamma ray. Commonly referred to as EM "Radiation," these waves have wavelengths ranging from several thousandkilometres ( m) to sub-picometres ( m).The wave is actually made up of two components which are perpendicular to the direction of the wave. EM radiationcan be thought of as particles (the photon) or waves, which is commonly referred to as the "wave particle duality"

The Speed of LightAll electromagnetic waves travel at the same speed (in a vacuum), and that is the universal constant known as the"speed of light," most often abbreviated by the lower-case letter "c".The speed of light is (exactly):c = 299 792 458 orc = 983 571 056

Visible LightIn the middle of the electromagnetic spectrum is visible light, i.e., the range that the human eye has evolved toobserve. The following is a chart of the wavelengths of visible light.

Colour Wavelength (m)

near ultraviolet 3.0 e -7

shortest visible blue 4.0 e -7

blue 4.6 e -7

green 5.4 e -7

yellow 5.9 e -7

orange 6.1 e -7

longest visible red 7.6 e -7

near infra-red 1.0 e -6

(Table 9.1, Griffiths)

A-level Physics/Electrons and Photons/Electromagnetic waves 21

Useful EquationsTo find out the energy of a particular EM wave, or its frequency one can use the several forms of the EinsteinEquation.First, to determine an EM wave frequency, from it's wavelength, . The wavelength multiplied by the frequencyis always a constant value: the speed of light, . Hence,

(1) c = ,

so you can find the frequency from the wavelength, or vice versa from simply manipulating this relationship.Next, to determine the energy from a smallest quantity of EM wave (photon). Here, we must introduce anotheruniversal quantity known as "Planck's Constant," most commonly abbreviated by a lower-case "h." Planck's constantis

h = 6.626068 e -34 .

With this in place we can use the "Planck Equation," which provides a relationship between the frequency, andenergy of a photon. The relation is as follows:

(2) E = h .

Now, if we only have the wavelength with which to start, we can manipulate equation (1) to get what we need.

(1) c = ,

,

(2) E = h c / .

References(In order of Mathematical/Material Depth)Halliday D.; Resnick R.; Walker J.; Fundamentals of Physics, Part 4: Chapters 34 - 38. 6th ed. John Wiley &Sons, Inc., 2003. Chapter 34.Griffiths, David J. Introduction to Electrodynamics. 3rd ed. Upper Saddle River, NJ: Prentice-Hall, Inc., 1999.Chapter 9, p364-411.Rybicki, G.; Lightman, A. Radiative Processes in Astrophysics. Wiley-Interscience, 1985.

A-level Physics/Wave properties/Reflection and Refraction 22

A- level Physics/ Wave properties/ Reflection andRefraction

Definitions and units• Frequency (f) — the number of complete oscillations of a particle each second.

• Frequency is measured in hertz (Hz). 1 Hz = 1 complete cycle per second.• Period (T) — the time taken for one complete oscillation.

• Period is usually measured in seconds, especially when used in equations.• Amplitude (A) — the maximum displacement of a particle from its equilibrium position.• Wavelength (λ) — the shortest distance between two parts of the same wave that are oscillating in phase with

each other.

Relationship between f and T

and hence,

Wave speedThe speed of a wave (v) is just the distance the wave has travelled over the time. If we take the time to be one period,then the distance will be one wavelength. Hence the speed of the wave is given by:

Using the fact that,

we can re-arrange the above equation to give

Laws of reflectionAngle of Incidence = Angle of ReflectionThe incident ray, reflected ray and the normal to the surface at the point of incidence are all in the same plane.

Refractive indexWhen light passes from one material to another the refractive index is the ratio of the speeds of light in the twomaterials.Refractive Index = Speed in Air / Speed in Medium

A-level Physics/Wave properties/Reflection and Refraction 23

Snell's LawSnell's law is the simple formula used to calculate the refraction of light when travelling between two media ofdiffering refractive index.

A- level Physics/ Wave properties/ Waves

Electromagnetic WavesThe electromagnetic spectrum is a family of waves that share the following properties:• They are able to transmit through a vacuum.• They all travel at the same speed in a vacuum (3×108 ms-1).• They are all transverse waves consisting of magnetic and electric fields oscillating at right angles to each other.• They all transfer energy as photons (the higher the frequency of a particular radiation the greater the energy

contained in each photon.• They can all be reflected, refracted, diffracted and create interference patterns.• Properties of these waves change with their frequency / wavelength so they are divided into seven sub groups

which are radio wave, microwaves, infra red waves, visible light, ultraviolet, x rays and gamma rays.Radio Waves

Radio waves are used mainly in communication over short or long distances. Shorter wavelengths are used fortelevision and FM radio while longer wavelengths are used for AM radio.Long Wave Wavelength = 1*104mMedium Wave Wavelength = 1*102mShort Wave Wavelength = 1*100mMicrowaves

Some microwaves pass easily through Earths atmosphere and are used for communications with satellites and ormobile phones.Microwaves are also commonly used for cooking with the aid of a microwave oven.Typical Values are as follows: Wavelength (m) = 3*10-2 Frequency (Hz) = 1*1010 Definitions Transverse Wave The direction of energy transfer is at 90 degrees to the direction of the vibrating particles. Longitudinal Wave The particles vibrate backwards and forwards along the line of the direction of the energy transfer in the wave. Amplitude The greatest displacement of the wave. Period (T) Is the time taken (in seconds) for one complete cycle of the wave. Frequency (f) The number of cycles of the wave per second. Wavelength (λ)

A-level Physics/Wave properties/Waves 24

The shortest distance between 2 particles on the wave with the same phase. Speed of wave Distance travelled by the wave in one time period. (λ/T)

A- level Physics/ Wave properties/ SuperpositionWhen two waves are superimposed the displacement of the resultant wave is equal to the sum of the individualdisplacements.

Diffraction and interferenceDiffraction is the spreading out of waves as they pass through a narrow gap or obstacle. When light diffracts throughtwo slits, the relationship connecting the separation of the light sources (i.e., the separation of the slits), a, theseparation of the fringes of the interference pattern, x, the wavelength of the light and the distance of the screen fromthe sources, D is as follows:

SuperpositionAt a point where two or more waves meet, the instantaneous displacement is the vector sum of the individualdisplacement due to each wave at that point.

Coherencetwo waves are said to be coherent with each other if the path difference between them stays constant from the sourceupto the detection.they may or may not have same wavelengh, frequencies and amplitudes

MonochromaticWaves of a single wavelength or frequency are monochromatic.

Path DifferencePath difference = for constructive waves.

Path difference = for destructive waves.

(where n is an integer).

Formation of a stationary waveIt forms due to the superposition of wave travelling in 1 direction with a wave of equal amplitude and wavelengthtravelling in the opposite direction.

Stationary waves on a string occur when

25

Appendices

A- level Physics/ The SI System of UnitsSI units are used throughout science in many countries of the world. There are seven base units, from which allother units are derived.

Base unitsEvery other unit is either a combination of two or more base units, or a reciprocal of a base unit. With the exceptionof the kilogram, all of the base units are defined as measurable natural phenomena. Also, notice that the kilogram isthe only base unit with a prefix. This is because the gram is too small for most practical applications.

Quantity Name Symbol

Length metre m

Mass kilogram kg

Time second s

Electric Current ampere A

Thermodynamic Temperature kelvin K

Amount of Substance mole mol

Luminous Intensity candela cd

Derived unitsMost of the derived units are the base units divided or multiplied together. Some of them have special names. Youcan see how each unit relates to any other unit, and knowing the base units for a particular derived unit is usefulwhen checking if your working is correct.

Note that "m/s", "m s-1", "m·s-1" and are all equivalent. The negative exponent form is generally prefered, for

example "kg·m-1·s-2" is easier to read than "kg/m/s2".

Quantity Name Symbol In terms of other derivedunits

In terms of baseunits

Area square metre

Volume cubic metre

Speed/Velocity metre per second

Acceleration metre per secondsquared

Density kilogram per cubicmetre

Specific Volume cubic metre perkilogram

A-level Physics/The SI System of Units 26

Current Density ampere per squaremetre

Magnetic Field Strength ampere per metre

Concentration mole per cubic metre

Frequency hertz Hz

Force newton N

Pressure/Stress pascal Pa

Energy/Work/Quantity of Heat joule J N m

Power/Radiant Flux watt W

Electric Charge/Quantity of Electricity coulomb C s A

Electric Potential/Potential Difference/ElectromotiveForce

volt V

Capacitance Farad F

Electric Resistance Ohm

Electric Conductance Siemens S

Magnetic Flux weber Wb V s

Magnetic Flux Density Tesla T

Inductance henry H

Celsius Temperature degree Celsius °C K - 273.15

Luminous Flux lumen lm cd sr

Illuminance lux lx

Activity of a Radionuclide bequerel Bq

Distance Travelled in 1 day by a Camel train Camel Train Ct

PrefixesThe SI units can have prefixes to make larger or smaller numbers more manageable. For example, visible light has awavelength of roughly 0.0000005 m, but it is more commonly written as 500 nm. If you must specify a quantity likethis in metres, you should write it in standard form. As given by the table below, 1nm = 1*10-9m. In standard form,the first number must be between 1 and 10. So to put 500nm in standard form, you would divide the 500 by 100 toget 5, then multiply the factor by 100 (so that it's still the same number), getting 5*10-7m. The power of 10 in thisanswer, i.e,. -7, is called the exponent, or the order of magnitude of the quantity.

A-level Physics/The SI System of Units 27

Prefix Symbol Factor Common Term

peta P quadrillions

tera T trillions

giga G billions

mega M millions

kilo k thousands

hecto h hundreds

deca da tens

deci d tenths

centi c hundredths

milli m thousandths

micro µ millionths

nano n billionths

pico p trillionths

femto f quadrillionths

Homogenous equationsEquations must always have the same units on both sides, and if they don't, you have probably made a mistake. Onceyou have your answer, you can check that the units are correct by doing the equation again with only the units.For example, to find the velocity of a cyclist who moved 100 metres in 20 seconds, you have to use the formula

, so your answer would be 5 .

This question has the units , and should give an answer in . Here, the equation was correct, andmakes sense.Often, however, it isn't that simple. If a car of mass 500kg had an acceleration of 0.2 , you could calculatefrom that the force provided by the engines is 100N. At first glance it would seem the equation is nothomogeneous, since the equation uses the units , which should give an answer in . Ifyou look at the derived units table above, you can see that a newton is in fact equal to , and thereforethe equation is correct.Using the same example as above, imagine that we are only given the mass of the car and the force exerted by theengines, and have been asked to find the acceleration of the car. Using again, we need to rearrange it for

, and we now have the formula: . By inserting the numbers, we get the answer . You

already know that this is wrong from the example above, but by looking at the units, we can see why this is the case:

. The units are , when we were looking for . The problem is the fact that

was rearranged incorrectly. The correct formula was , and using it will give the correct answer

of 0.2 . The units for the correct formula are .

A-level Physics/Symbols for Physical Quantities 28

A- level Physics/ Symbols for Physical Quantities

Symbols for Physical Quantities

Latin LettersA

Amplitude, cross-sectional areaa

Accelerationc

The speed of light in a vacuum, about 3x108ms-1

dDistance

EEnergy, sometimes electromotice force

fFrequency

FForce

ggravitational acceleration (approx. 9.8ms-2)

GUniversal Gravitational Contant

I(Uppercase I)Current

l(Lowercase L)Length

mmass

Ppower

pmomentum

QCharge

rRadius of a circle/sphere

A-level Physics/Symbols for Physical Quantities 29

RResistance

tTime

TTemperature; time period for a single rotation or oscillation

uInitial velocity

vVelocity

VVolume, Voltage

WWeight, work

Greek LettersΔ

(capital delta)Change in (eg time)

(lowercase gamma)A photon

θ(theta)Angle, Temperature (celcius)

λ(lowercase lambda)Wavelength

ρ(rho)Resistivity

(phi)Work function

ω(lowercase omega)Angular velocity/frequency.

A-level Physics/Symbols for Physical Quantities 30

ResourcesBoise State University [1]

References[1] http:/ / selland. boisestate. edu/ jbrennan/ physics/ notes/ Introduction/ physics_symbols. htm

A- level Physics/ Equation SheetEquations, constants, and other useful data that the A-level student of physics is required to memorise.

Forces and motionSee also Symbols for Physical Quantities.

Newtonian MechanicsKinematic Equations

•

•

••

•

•

Force and Momentum

••

•

•

Work and Energy

• (for small heights only)

• (for any height)

•

•

•

Where:• = initial velocity• v = final velocity• a = acceleration

A-level Physics/Equation Sheet 31

• s = displacement• t = time• W = work done• m = mass• M = different mass, for equations with 2 masses interacting

A- level Physics/ Glossary of TermsDefinitions of keywords and terms that you will need to know.

Contents

Top - A B C D E F G H I J K L M N O P Q R S T U V W X YZ

AAbsolute zero

Zero on the thermodynamic temperature scale, or 0 K (kelvin), where a substance has minimum internalenergy, and is the coldest possible temperature. It is equal to -273.15 degrees Celsius.

AccelerationThe (instantaneous) rate of change of velocity in respects to time.

CCouple

Two equal, opposite and parallel forces which create rotational force.

DDisplacement

A vector quantity, the distance something is from its initial position, in a given directionDensity

Density is the mass of a body per unit volume

EEnergy

The stored ability to do workExtension (x)

The change in length of an object when a force is applied to it

FForce

A force causes a mass to change motion

A-level Physics/Glossary of Terms 32

GGravitational Potential Energy

the energy an object has due to its relative position above the ground. Found by mass x gravity (orgravitational field strength) x height

HHeat

is a form of energy transfer, also known as 'Thermal Energy'.Hookes Law

an approximation that states that the extension of a spring is in direct proportion with the load added to it aslong as this load does not exceed the elastic limit.

JJoule

The SI unit of work done, or energy. One joule is the work done when a force of one newton moves an objectone metre.

KKinetic Energy

The energy an object possesses due to its motion, given by KE = 0.5 x mass x velocity²

NNewton

Unit in which force is measured. Symbol "N". One Newton is the force required to give a mass of 1kg anacceleration of 1ms^-2

PPeriod (T)

The time taken for one complete oscillation. Denoted by 'T'. T=1/fPower

The rate at which work is done.Pressure

The load applied to an object per unit surface area.Potential difference

The work done in moving a unit positive charge from one point to the other. The unit is volt.

A-level Physics/Glossary of Terms 33

SScalar

A quantity with magnitude but no direction.Speed

A scalar quantity, speed = distance / timeNB s can also mean displacement.Stopping Distance

Stopping distance = Thinking distance + Braking distancethinking distance (distance traveled while reacting) = time taken to react X velocitybraking distance (distance traveled while braking)

TTerminal Velocity

maximum velocity a body can travel. When resistive forces = driving force, acceleration = 0, so it cannottravel any faster.

Torque / momentMoment = force x perpendicular distance from the pivot to the line of action of the forceTorque = one of the forces x the distance between them

UUpthrust

A force experienced due to the pressure difference of the fluid at the top and bottom of the immersed portionof the body.

VVector

A quantity with magnitude and direction.Velocity

The (instantaneous) rate of change of displacement with respect to time. Velocity is a vector.

A-level Physics/Glossary of Terms 34

WWork Done

The energy transferred when an object is moved through a distance by a force. Can be calculated bymultiplying the force involved by the distance moved in the direction of the force.

Alternatively, [work done = transfer of energy]. i.e, work is done when energy is transferred from one form toanother.

YYoung Modulus

Stress per unit Strain, units: Pascals or N/m2

A- level Physics/ Forces and Motion/ KinematicsKinematics is the study of the way objects move. It focuses on describing an object's motion, and doesn't explainhow forces affect it.

Distance and displacement

Although the distance covered is 25m, the displacement is 10m.

You may already be familiar with theterm distance, as the distance betweentwo points is the length of the path abody takes between those two points.

Distance is a scalar, so if you were towalk 10m North, and then 10m South,you would have covered a distance of20m.Displacement, however, is a vectorquantity. Displacement, in a sense, issimply the shortest distance betweenany two points. If a body ends up at thesame spot as its initial position aftertravelling through some distance, wesay that the displacement of the body is0, so the above example would give you a total displacement of 0m.

In the diagram on the right, if the distance covered was 25m, then the displacement would be 10m. You can find thedisplacement by measuring the length of the line between the start and end points.A measurement is a displacement if it has a specified direction, otherwise it is a distance.The symbol for distance is d, and the symbol for displacement is s or x. Be careful not to confuse the s fordisplacement with s for seconds.

A-level Physics/Forces and Motion/Kinematics 35

Speed and velocityThe speed of an object is the distance it moves in a unit of time.You can find the speed of an object if you know the distance an object moved, and the time it took to move thatdistance:

, or .

Velocity is a vector, and similar to the difference between distance and displacement, velocity is speed in a specifieddirection.A vehicle could be moving with constant speed, but have a changing velocity. This happens when the vehicle turns.Imagine a racing car is moving along the track with a speed of 20m s-1. If this direction is taken to be positive, thenthe car's velocity is also 20m s-1. Now, if the car was to turn into a "U" bend, its velocity would change. When thecar is perpendicular to the first straight, the car will still have a speed of 20m/s-1, but its velocity will now be 0m/s-1.When the car has made the turn and is coming back to the starting point, the speed is still 20m/s-1, but the velocity is-20m/s-1, since the car is now moving in the opposite direction.The symbol for speed is s, and the symbol for velocity is v. Be careful not to confuse the s for speed with s fordisplacement or s for seconds.

AccelerationAcceleration is the rate of change of velocity. In other words, acceleration is the amount an object's velocity changesin a unit of time.If you know the change in velocity and the time the change took, you can find acceleration using the formula:

, or .

Alternatively, if you have the initial and final velocities, you can use the formula:

, where is the initial velocity, and is the final velocity.

(Delta) means "change in".Acceleration is a vector, and can slow down objects as well as speed them up. An object will slow down when itsacceleration is opposite to its velocity. The object is now decelerating.Something can be said to be accelerating if it's changing direction. In the example above, the car changes its velocityby turning a corner. Since acceleration is the rate of change of velocity, the car is accelerating.

Acceleration is measured in metres per second per second, or . If something had an acceleration of , it means that its speed increases by each second.

A-level Physics/Forces and Motion/Kinematics 36

Graphs

Measuring speed and acceleration

Light gatesThe Light Gate has an infrared transmitter and receiver, mounted in a robust steel housing avoids any misalignmentproblems. The Light Gate can be used for studying free fall, air track and incline plane experiments.

Ticker tape timerThe ticker tape timer is used in the measurement of velocity acceleration and general timing. It has a frequency of 50to 60Hz (varies according to type) equivalent to that of the mains power supply. It will give good results if operatedfrom a 12V a.c. power supply. The timer uses an electromagnet which activates a striker producing dots via a carbondisk on the ticker tape. At 50Hz, each dot will represent 0.02seconds.While at 60Hz, one dot represents 0.01seconds.

AccelerometerThis device is used for the measurement of acceleration and the unit is in metre per second square (m/s2)

The equations of motionFrom the definitions of position, velocity and acceleration, one can derive the relationships between the threevectors.

•

•

•Where is acceleration in the direction of the velocity, is displacement, is time, is initial velocity and is final velocity. Note that these equations only work when an object has constant acceleration and the direction ofmotion is linear.

Deriving the equationsAs stated above, the equations of motion are derived from:

.

Deriving

The expression is the average velocity during the time frame. This is allowed only in a linear context; non

linear kinematics requires the use of calculus. Because the average velocity accounts for the variations of thevelocities during a linear change, the total distance traveled is thus the velocity during the time frame multiplied bythe time.

A-level Physics/Forces and Motion/Kinematics 37

Deriving s = ut + 1/2 a(Δt)2

This equation is derived from the equations and .

Substitute into the equation

=

=

=

An alternative derivation that is more commonly used is done by Calculus. Assuming

•

•

•

•

• the boundary condition is that at t = 0, \Delta s = 0 so C = 0. Thus the equation becomes

•

Deriving v2 = u2 + 2aΔs

This equation is derived from the equations and .

Multiply by

Deriving the equations in vectors• All constant are taken in capital letters• All variable are given in small letter

Deriving v(t) = Ui + A (t - T

i)

so

for zero or constant acceleration A we have

A-level Physics/Forces and Motion/Kinematics 38

we have one unknown K , we need to consider initial or final condition

• Lets take initially we have

ie

If we take final condition in consideration then i.e.:

constant acceleration can be found using initial and final condition

Deriving s(t) = Si + U

i(t-T

i) + (1/2)A (t - T

i)2

now we have

for eliminating K we need either final or initial condition i.e.

If we would have taken final condition ie then

A-level Physics/Forces and Motion/Kinematics 39

Deriving |v(t)|2 = |Ui|2 + 2 A . (s(t)-S_i)

taking case for final velocity

or

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