AP Physics 2 Unit Notes

Fluids

  • Fluids are substances that can flow, typically liquids and gases, due to their weaker interatomic forces compared to solids.

Density

  • Density is the mass per unit volume of a substance, a positive scalar quantity.
  • Formula: p = \frac{m}{V}
    • where p is density, m is mass, and V is volume.
  • SI unit: kg/m³
  • C.G.S unit: g/cc
  • Example: If 10^-3 m³ of oil has a mass of 0.8 kg, then the density is:
    • p = \frac{0.8}{10^{-3}} = 800 \text{ kg/m}^3

Pressure

  • Pressure is the magnitude of the normal force acting per unit surface area.
  • Formula: P = \frac{F}{A}
    • where P is pressure, F is force, and A is area.
  • S.I unit: Pascal (Pa), where 1 Pa = 1 N/m²
  • Practical units: atmospheric pressure (atm), bar, torr
    • 1 atm = 1.01325 x 10^5 Pa = 1.01325 bar = 760 torr = 760 mm of Hg
  • Example: A cement column with base area 0.5 m² and height 2 m. The density of cement is 3000 kg/m³.
    • Force exerted on the ground is equal to its weight, mg.
    • m = pV = pAh = (3 \times 10^3 \text{ kg/m}^3)(0.5 \text{ m}^2)(2 \text{ m}) = 3 \times 10^3 \text{ kg}
    • P = \frac{F}{A} = \frac{mg}{A} = \frac{(3 \times 10^3 \text{ kg})(10 \text{ N/kg})}{0.5 \text{ m}^2} = 6 \times 10^4 \text{ Pa} = 60 \text{ kPa}

Hydrostatic Pressure

  • Hydrostatic pressure is the pressure due to a liquid, dependent on the density of the liquid and the depth below the surface.
  • Formula: P{\text{liquid}} = \frac{\text{force}}{\text{area}} = \frac{F{\text{g liquid}}}{A} = \frac{p(lwh)g}{lw} = pgh
    • where p is density, g is the acceleration due to gravity, and h is the depth.
  • Total (absolute) pressure: P{\text{total}} = P0 + P{\text{liquid}} = P{\text{atm}} + pgh
    • P_{\text{total}} is the total pressure when the tank is open to the atmosphere.

Buoyancy

  • Buoyancy is the upward force exerted by a fluid on a body that is fully or partially immersed in the fluid.
  • Buoyant force formula: F{\text{buoy}} = p{\text{fluid}} V_{\text{sub}} g
    • Archimedes' principle is used.
    • \frac{V{\text{sub}}}{V} = \frac{p{\text{object}}}{p_{\text{fluid}}}
  • Example: An object with mass 150 kg and volume 0.75 m³ is floating in ethyl alcohol with a density of 800 kg/m³.
    • Density of the object: p_{\text{object}} = \frac{m}{V} = \frac{150 \text{ kg}}{0.75 \text{ m}^3} = 200 \text{ kg/m}^3
    • Ratio of object density to fluid density: \frac{p{\text{object}}}{p{\text{fluid}}} = \frac{200 \text{ kg/m}^3}{800 \text{ kg/m}^3} = \frac{1}{4}
    • [\frac{1}{4}] of the object's volume is below the surface, so the fraction above the surface is 1 - \frac{1}{4} = \frac{3}{4}

The Continuity Equation: Flow Rate and Conservation of Mass

  • Volume Flow Rate is the volume of fluid that passes through a particular point per unit of time.
  • Formula: f = Av
    • where f is the volume flow rate, A is the cross-sectional area, and v is the flow speed.
  • S.I unit: m³/s
  • The Continuity Equation: A1v1 = A2v2 if the density is constant.
  • Example: A circular pipe with non-uniform diameter carries water. At one point, the radius is 2 cm and the flow speed is 6 m/s.
    • The volume flow rate is: f = A1v1 = \pi r1^2 v1 = \pi (0.02 \text{ m})^2 (6 \text{ m/s})
    • If the pipe constricts to a radius of 1 cm, the flow speed is determined by A1v1 = A2v2.
    • v2 = \frac{A1v1}{A2} = \frac{\pi r1^2 v1}{\pi r2^2} = v1 \left( \frac{r1}{r2} \right)^2 = (6 \text{ m/s}) \left( \frac{2 \text{ cm}}{1 \text{ cm}} \right)^2 = 24 \text{ m/s}

Bernoulli's Equation: Conservation of Energy in Fluids

  • Assumptions:
    • The fluid is incompressible.
    • The fluid's viscosity is negligible.
    • The fluid is streamlined.
  • Equation: P + pgy + \frac{1}{2} pv^2 = \text{constant}
    • An alternative way of stating Bernoulli's equation P1 + pgy1 + \frac{1}{2} p{v1}^2 = P2 + pgy2 + \frac{1}{2} p{v2}^2
    • Where P is pressure, p is density, g is the acceleration due to gravity, y is elevation, and v is velocity. A1, A2: Cross-sectional areas at points 1 and 2. P1, P2: Pressures. v1, v2 : Velocities. h1, h2,: Elevations
  • Example: Water is pumped through a pipe whose cross-sectional area decreases to ⅓ at the exit point. If y = 60 cm and v_1 = 1 m/s, what is the gauge pressure at Point 1?
    • Apply Bernoulli's equation to point 1 and the exit point, point 2.
    • Set point 1 as the horizontal reference level, making y_1 = 0.
    • Since the area decreases by a factor of 3, the flow speed increases by a factor of 3, so v2 = 3v1.
    • The pressure at 2 is P{\text{atm}}. Bernoulli's equation becomes P1 + \frac{1}{2} pv1^2 = P{\text{atm}} + pgy2 + \frac{1}{2} p{v2}^2

Bernoulli's Effect

  • At comparable heights, the pressure is lower where the flow speed is greater.
  • Equation: P1 + \frac{1}{2} pv1^2 = P2 + \frac{1}{2} pv2^2
  • Application: Air flow over an airplane wing. The air on the bottom has greater pressure and pushes up on the wing giving the airplane lift force.

Thermodynamics

  • Thermodynamics deals with the exchange of heat energy between bodies and the conversion of heat energy into mechanical energy and vice versa.
  • Heat: The thermal energy transmitted from one body to another; energy in transit.
  • Temperature: A measure of an object's internal energy.

The Kinetic Theory of Gases

  • Relates to the macroscopic properties of gases such as pressure, temperature, etc.
  • Every gas consists of small particles known as molecules.
  • Molecules of a gas are identical but different from those of another gas.
  • The volume of molecules is negligible in comparison to the volume of gas.
  • The density of gas is constant at all points.
  • Pressure is exerted by gas molecules on the walls of the container.
  • No attractive or repulsive forces exist between the gas molecules.

The Ideal Gas Law

  • Applies to gases showing ideal behavior; cannot be applied to real gases.
  • Equation: PV = nRT
    • P = Pressure
    • V = Volume
    • n = Number of Moles of Gas
    • R = Universal Gas Constant (8.314 J/mol.K)
    • T = Temperature
  • Also written as: PV = NkBT, where kB is Boltzmann's constant.
  • The average kinetic energy is given by: K{\text{avg}} = \frac{3}{2}kBT
    • Note: Use Kelvins as your temperature unit
  • Root Mean Square Velocity v{\text{rms}} = \sqrt{\frac{3kBT}{m}}
  • Example: In order for the rms velocity of the molecules in a given sample of gas to double, what must happen to the temperature?
    • Since v_{\text{rms}} is proportional to the square rooth of T, the temperature must quadruple, again, assuming the temperature is given in kelvins.
  • Example: A cylindrical container of radius 15 cm and height 30 cm contains 0.6 mole of gas at 433 K. How much force does the confined gas exert on the lid of the container?
    • The volume of the cylinder is \pi r^2 h, where r is the radius and h is the height.
    • Using the Ideal Gas Law to find P
      • P = \frac{nRT}{V} = \frac{(0.6 \text{ mol})(8.31 \text{ J/mol} \cdot \text{K})(433 \text{ K})}{\pi (0.15 \text{ m})^2 (0.30 \text{ m})} = 1.018 \times 10^5 \text{ Pa}
    • Since the area of the lid is \pi r^2, the force exerted by the confined gas on the lid is:
      • F = PA = (1.018 \times 10^5 \text{ Pa}) \cdot \pi (0.15 \text{ m})^2 = 7,200 \text{ N}
  • Pressure difference explains why the lid isn't blown off. Confined gas exerts force upward, the atmosphere exerts a force downward. The net force on the lid is Fnet = (ΔP)A = (0.005×105 Pa)∙𝜋(0.15 m)2=35 N

The Maxwell-Boltzmann Distribution

  • The Kinetic theory of gases applies to a large number of particles.
  • Some molecules will be moving faster than average and some much slower.

The Laws of Thermodynamics

Zeroth Law of Thermodynamics

  • If objects 1 and 2 are in thermal equilibrium with Object 3, then Objects 1 and 2 are in thermal equilibrium with each other.

First Law of Thermodynamics

  • It is a special case of the law of conservation of energy that describes processes in which only internal energy changes and the only energy transfers are by heat and work.
  • Equation: \Delta U = Q + W
    • where \Delta U is the change in internal energy, Q is the heat added to the system, and W is the work done on the system.
  • Work done: (W = -P\Delta V)

Thermodynamic Processes

  • Isothermal: Temperature remains constant.
  • Adiabatic: No transfer of heat.
  • Isobaric: Pressure remains constant.
  • Isochoric: Volume remains constant.

Second Law of Thermodynamics

  • It describes how systems evolve over time.

  • Entropy increases i.e. randomness, disorder, or uncertainty.

  • Heat always flows from an object at a higher temperature to an object at a lower temperature, never the other way around.

  • Example: Whatʼs the value of W for the process ab following path 1 and for the same process following path 2 (from a to d to b), shown in the P–VP– V diagram below?

    • Path 1:
      • Since the P remains constant, the work done is -PΔV
      • W = -P\Delta V = -(1.5 \times 10^5 \text{ Pa}) [(30 \times 10^{-3} \text{ m}^3) - (10 \times 10^{-3} \text{ m}^3)] = -3,000 \text{ J}
    • Path 2:
      • Gas is brought from state aa to state bb, along path 2, then work is done only along the part from aa to dd. From dd to bb, the volume of the gas does not change, so no work can be performed.
        *Area under the graph from aa to dd is
      • W = -\frac{1}{2} h(b1 + b2) = - \frac{1}{2} (\Delta V) (Pa + Pd) = - \frac{1}{2} (20 \times 10^{-3} \text{ m}^3) [(1.5 \times 10^5 \text{ Pa}) + (0.7 \times 10^5 \text{ Pa})] = -2,200 \text{ J}

Heat Engines

  • A device which uses heat to produce useful work. For any cyclic heat engine, some exhaust heat is always produced.
  • It’s impossible to completely convert heat into useful work.
  • Energy in the form of heat comes into the engine from a high-temperature source, some of this energy is converted into useful work, the remains are ejected as exhaust heat. Then, the cycle returns to its original state and the cycle resumes again.
  • Example: A heat engine draws 800 J of heat from its high-temperature source and discards 450 J of exhaust heat into its cold-temperature reservoir during each cycle. How much work does this engine perform per cycle?
    • The absolute value of the work output per cycle is equal to the difference between the heat energy drawn in and the heat energy discarded:
      • |W| = QH - |QC| = 800 \text{ J} - 450 \text{ J} = 350 \text{ J}

Heat Transfer

  • There are three ways in which the heat is transferred:
    • Conduction
    • Convection
    • Radiation

Conduction

Radiation

  • Heat conducts from one point to another only if there is a temperature difference between the two objects.
  • The rate at which heat is transferred is given by:
  • \frac{Q}{\Delta t} = kA \frac{\Delta T}{L}

Convection

  • The movement caused within a fluid by the tendency of hotter and therefore less dense material to rise, and colder, denser material to sink under the influence of gravity, which consequently results in the transfer of heat.

Radiation

  • Emission or transmission of energy in the form of waves or particles through space or through a material medium.

Electric Force, Field, and Potential

Electric Charge

  • In an isolated system, charge is always conserved.
  • Protons and electrons have a quality called electric charge.
  • Charge is invariant in nature (value of charge doesn’t depend on frame of reference).
  • Charge is quantized (it means any charge on the body is an integral multiple of the fundamental amount of electric charge).
  • Q = ne
    • e = 1.6 \times 10^{-19} \text{ C}

Coulomb's Law

  • Electric force between two particles with charges q1 and q2, separated by distance r, has a magnitude given by:
  • F = k \frac{|q1q2|}{r^2}
    • k_0 = 9 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2
  • k = \frac{1}{4\pi \epsilon_0}

Electric Field

  • The space is surrounded by a charge in which another charged particle experiences the force.
  • The electric field vector E:
    • \vec{E} = \frac{\vec{F}}{q}
    • where \vec{F} is the electric force experienced by the charge q.
  • The strength of the electric field created by a point-charge source of magnitude Q.
    • E = k \frac{|Q|}{r^2}
  • Types of electric fields:
    • Radial field: occurs from a point charge/charged sphere. Inversely proportional to the square of the distance from the point charge.
    • Electric fields due to many point charges: The results in an electric field are determined by superposition.
    • Infinite sheet of charge: the electric field is constant in both magnitude and direction.
  • Electric field lines never cross.
  • Electric field lines always point away from positive source charges and toward negative ones.
  • Electric field is always perpendicular to the surface, no matter what shape the surface may be.
    Example:
  • A charge q = +3.0 \text{ nC} is placed at a location, at which the electric field strength is 400 N/C. Find the force felt by the charge q.
    • \vec{F} = q\vec{E} = (3 \times 10^{-9} C) (400 N/C) = 1.2 \times 10^{-6} N.

The Uniform Electric Field

  • A lot of problems deal with uniform electric fields.
  • Uniform field signifies the constant force.

Conductors and Insulators

Conductors:

  • Materials that generally allow the flow of excess charge without resisting it.
  • Metals, aqueous solutions, etc.

Insulators

  • Materials which resist the flow of electrons.
  • Glass, rubber, wood, and plastic.

Methods of Charging

Through Charging by Friction

  • It involves rubbing the insulator against another material, thereby stripping electrons from one to another material.

Through Conduction

  • When we connect two conductors charge flows from one to another until the potential of both the conductors becomes the same.

Through Induction

  • The process of charging by induction may be used to redistribute charges among a pair of neutrally charged spheres.
  • In the end, both spheres are charged.

Electrical Potential Energy

  • If W_E is the work done by the electric force, then the change in the charge’s electrical potential energy is defined by:
    • \Delta U = -W_E
  • Example: A positive charge +q moves from position A to position B in a uniform electric field E: What is its change in electrical potential energy?
    • The electric force that the charge feels, F_E = qE, is constant.
    • The work done by field equal to W_e = FEr = qEr, so the change in the electrical potential energy is \Delta U = -qEr

Electrical Potential Energy from a Point Charge

  • Electrical potential energy required to move along the field lines surrounding a point charge is given by:
    • U = k \frac{qQ}{r}

Electric Potential

  • It is a scalar property of every point in the region of the electric field.

  • At a point in the electric field potential is defined as the interaction of a unit positive charge

    • V = \frac{U}{q}

Electric Potential of a uniform field

  • Example: Consider a very large, flat plate that contains a uniform surface charge density σ. At points that are not too far from the plate, the electric field is uniform. What is the potential at a point which is a distance d from the sheet (close to the plates), relative to the potential of the sheet itself?
    • \Delta V = -Ed = -\frac{\sigma}{2\epsilon_0}d

Capacitors and Capacitance

  • Capacitor: Two conductors, separated by some distance that carries equal but opposite charges +Q and -Q. The pair comprises a system called a capacitor.
  • Parallel-Plate capacitor: The capacitor is in the form of parallel metal plates or sheets.

Capacitance

  • Q is the total charge stored on either plate of a capacitor, and \Delta V is the potential difference between the plates.
  • The ratio of Q to \Delta V, for any capacitance, is defined as its capacitance.
  • C = \frac{Q}{\Delta V}

Electric Field and Capacitors

  • The electric field E always points from the positive plate towards the negative plate, and the magnitude remains the same at every point between the plates.

Energy stored in Capacitor:

  • U = \frac{1}{2} QV = \frac{1}{2} CV^2 = \frac{Q^2}{2C}

Capacitors and Dielectric

  • To keep the plates of the capacitor apart they are filled with a dielectric which increases the capacitance of the capacitor.

Electric Circuits

Electric Current

  • It comprises an energy source typically a battery, one or more conducting materials, and circuit components such as resistors and capacitors.
  • Continuous flow of charge
  • Current is the charge per unit of time expressed in coulombs per second (ampere)
  • Average Current:
    • I = \frac{Q}{t}

Battery and Voltage

  • A battery is a device that maintains an electric potential difference between the two terminals.
  • The battery could consist of a single cell or multiple cells.
  • A voltage difference between two points in a conducting material causes a charge to flow.
  • The voltage is measured in volts.
  • As long as the potential difference is maintained, the flow of charge will continue.
  • The flow is from higher potential to lower potential.
  • The electricity also flows in that direction called direct current.

Resistors and Resistance

  • Resistance: It is the impedance to the flow of electricity through a material.
  • As a charge moves through a material, it eventually hits a non-moving nucleus in the material.

Resistivity

  • It can be thought of as the density of nuclei the electrons may strike.
  • R = \rho \frac{l}{A}
  • This equation is applied to shapes with uniform cross-sectional areas and cannot be applied to those with varying cross-sectional areas.
  • Example: A wire of radius 1 mm and length 2m is made of platinum(resistivity = 1 × 10−7Ω·m).

Measurement Units:

  • Resistance is measured in ohms (Ω)
  • Resistivity is measured in ohm-meters (Ωm)

Combining Resistors and Equivalent Resistance

  • Equivalent resistance: When two or more resistors are combined mathematically, the resulting resistance is called equivalent resistance.
  • In arrangements of three or more resistors, it is possible for the arrangement to be a mixture of series and parallel.

Resistors in Series

  • Resistors arranged in series result in an overall resistance that is greater than the resistance of any individual resistors in the arrangement.
  • R{eq} = R1 + R_2 + … Example:
    • A resistor having an electrical resistance value of 100 ohms, is connected to another resistor with a resistance value of 200 ohms. The two resistances are connected in series. What is the total resistance across the system?
    • R1 = 100 ohm, R2 = 200 ohm, Req = R1 + R2 = 300 ohm.

Resistors in Parallel

  • Resistors arranged in parallel result in an overall resistance that is less than any of the resistors.
  • \frac{1}{R{eq}} = \frac{1}{R1} + \frac{1}{R_2} + …

Measuring Current and Voltage in a circuit

  • Ammeter: It is a device with a very low resistance that measures the current.
  • Voltmeter: It measures the electric potential difference called the potential drop.

Ohm's Law

  • V = IR

    • R is the resistance in the circuit.
    • V is the potential difference in the circuit
    • I is the electric current

Power Dissipation

  • The power dissipated by a circuit component is given by the product of the current through the component and the voltage drop across it.
    • P = VI = I^2R = \frac{V^2}{R}
    • Note: P is the power, V is the potential difference in the circuit and I is the electric current

Kirchhoff's Law

  • Used when analysing the circuits.
  • The loop rule states that the voltage drop across any complete loop in a circuit is 0V.
  • The junction rule states that the sum of all current flowing into any junction is equal to the current flowing out of the junction.

EMF and internal Resistance

  • The voltage supplied by an ideal battery is referred to as EMF (electromotive force).
  • A battery in a circuit can be modelled as an ideal EMF in series with a resistor.
  • In this model, r is called the internal resistance of the battery.
  • The voltage measured across the EMF source is called the terminal voltage.

Capacitors in the circuit

  • A capacitor stores energy in an electric field. A parallel-plate capacitor consists of two plates of area A and separation d.
  • Capacitance determines the amount of charge that can be stored on the plates for a given voltage
    • C = k \varepsilon_0 \frac{A}{d}
    • Capacitance is measured in a unit called farad.
  • The ratio of the charge on either plate to the voltage across the plates is capacitance.
    • \Delta V = \frac{Q}{C}

RC Circuits with Capacitors in Steady State

  • When a capacitor is discharged, the voltage between the plates is 0V and it acts like a wire.
  • The discharged capacitor short circuits any resistors arranged in parallel with the capacitor.
  • The situation is reversed when the capacitor is fully charged which then acts like a broken wire.
  • The fully charged capacitor short circuits and resistors arranged in series with the capacitor.

Magnetism and Electromagnetic Induction

Magnetic Field

  • The space surrounding a magnet is called a magnetic field.
  • The direction is defined as pointing out of the north end of a magnet and into the south end of a magnet.
  • We use (x) when the magnetic field goes into the plane.
  • We use (.) when the magnetic field goes out of the plane.
  • There are no monopoles as they always exist in pairs.

Bar Magnets

  • A permanent bar magnet creates a magnetic field that closely resembles the magnetic field produced by a circular loop of current-carrying wire.
  • The magnetic field created by a permanent bar magnet is due to the electrons.
  • All materials have some magnetic permeability which determines how great a magnetic field an object will develop.
    *Magnetic poles repel each other when they are the same and opposite poles attract each other.

The Magnetic Force on a Moving Charge

  • If a particle with charge q moves with velocity v through a magnetic field B, it will experience a magnetic force, Fb:
    • F_B=qv∗B
    • Magnitude: F_B=∣q∣vBsin𝜃
    • If angle = 90 degrees, it is the max value.
    • If 0 or 180, the velocity and magnetic field are parallel or antiparallel, then the magnetic force is zero.

Right-Hand Rule

  • Whenever you use the right-hand rule, follow these steps:
    • Orient your hand so that your thumb points in the direction of the velocity v. If the charge is negative, turn your thumb by 180 degrees.
    • Point your fingers in the direction of B.
    • The direction of FB will then be perpendicular to your palm.

The Magnetic Force on a Current-Carrying Wire

  • Let a wire of length l be immersed in magnetic field B. If the wire carries current I, then the force on the wire is \vec{F_B} = I\vec{l} \times \vec{B}
    • F_B = BIl \sin{\theta}

Magnetic Fields Created by Current-Carrying Wire

  • Magnetic fields are unending loops. The direction of the circles is determined by the right-hand rule.
    • B=\frac{\mu_0 I}{2\pi r}
      • \mu_0 is the permeability of free space
      • \mu_0 = 4\pi \times 10^{-7} = N/A^2 = 4\pi \times 10^{-7} T∗m/A

Right-Hand Rule for the Magnetic Field created by a Current-Carrying Wire

  • Put your thumb in the direction of current or in direction of a positive travelling charge.
  • Grab the wire/path.
  • As the fingers curl around your thumb, it represents the magnetic field going around the wire/path.

Solenoids Create Uniform Fields

  • Solenoid is a device that is constructed by a series of coaxial wires through which a continuous current flows.
  • When there is no current, there is no magnetic field.

Motional EMF

  • The simple act of moving a conducting rod in the presence of an external magnetic field creates an electric field within the rod.
  • Induced Current: An induced current is created in three ways:

Changing the area of the loop of wire in a stationary magnetic field

Changing the magnetic field strength through a stationary circuit

Changing the angle between the magnetic field and the wire loop

Faraday's Law of Electromagnetic Induction

  • Electromotive force can be created by the motion of a conducting wire through a magnetic field.

  • A current is induced when the magnetic flux passing through the coil or loop of wire changes.

  • Magnetic flux equation: \Phi_B = B \cdot A= BA\cos\theta

Faraday's Law

  • |\varepsilon{avg}| = |\frac{\Delta \PhiB}{\Delta t}|

Lenz's Law

  • The induced current will always flow in the direction that opposes the change in magnetic flux that produced it.

    • \varepsilon{avg} = -\frac{\Delta \PhiB}{\Delta t}

Geometric and Physical Optics

Introduction

  • Electromagnetic Waves range from radio waves to gamma rays.
  • EM waves can propagate through empty space.
  • It consists of time-varying electric and magnetic fields that oscillate perpendicular to each other and to the direction of propagation of the wave.
  • c = 3 x 10^8 m/s
    • v = f \lambda
  • An oscillating charge generates an electromagnetic wave.
  • EM waves are transverse waves.
  • The direction in which the waveʼs electric field oscillates is called the direction of polarization of the wave.
  • EM waves do not require a medium to propagate.

The Electromagnetic Spectrum

  • It can be categorized by its frequency.
  • The full range of waves is called the electromagnetic spectrum.

Interference and Diffraction

  • The waves experience interference when they meet.
  • They interfere destructively or constructively depending on their relative phase.
  • They meet in phase (crest meets crest): combine constructively
  • They meet out of phase (crest meets trough): and combine destructively.
  • Waves are assumed to be coherent (which means their first phase difference remains constant over time and does not vary).

Young's Double Slit Experiment

  • The incident light on a barrier that contains two narrow slits, separated by distance d.
  • On the right there is a screen whose distance from the barrier L, is much greater than d.

Diffraction

  • The alteration in the straight-line propagation of a wave when it encounters a barrier is called diffraction.
  • The waves will diffract through the slits spread out, and interfere as they travel towards the screen.