IB Physics SL HL 1 Study Guide

IB Physics SL/HL 1 Study Guide Fundamental Constants: Quantity / Symbol - Acceleration of free fall / g - Gravitational constant / G - Avogadro’s constant / 𝑁𝐴 - Gas constant / R - Boltzmann’s constant / 𝑘𝐵 - Stefan-Boltzmann constant / 𝜎 - Coulomb constant / k - Permittivity of free space / 𝜖0 - Permeability of free space / 𝜇0 - Speed of light in vacuum / c - Planck’s constant / h - Elementary charge / e - Electron rest mass / 𝑚𝑒 - Proton rest mass / 𝑚𝑝 - Neutron rest mass / 𝑚𝑛 - Unified atomic mass unit / u - Solar Constant / S - Fermi radius / 𝑅0 Measurement - SI Units- Standard units of measurements consisting of the following: - Length/ Meter/ m - Time/ Seconds/ s - Amount of substance/ Mole - Electric Current/ Ampere/ A - Temperature/ Kelvin/ K - Luminous Intensity/ Candela/ cd - Mass/ Kilogram/ kg From here, units are derived, such as Joules, which is force∗distance, so 𝑁 ∗ 𝑚 Kinematics in One Direction - Position of a particle is the position in respect to the origin, the unit being “s” - This is called displacement, different from distance - Displacement is a vector quantity, if it’s positive it has moved in the positive direction, and if it’s negative it has moved in the negative direction 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 - 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑆𝑝𝑒𝑒𝑑 = - Instantaneous Velocity is the velocity at the given moment 𝑇𝑜𝑡𝑎𝑙 𝑇𝑖𝑚𝑒 𝑣 = 𝑙𝑖𝑚𝛥𝑡→0 - 𝛥𝑥 𝑑𝑥 = 𝛥𝑡 𝑑𝑡 Average Acceleration 𝑎𝑎𝑣𝑔 = 𝛥𝑣 𝛥𝑡 - Average Velocity - 𝛥𝑥 𝑥2 − 𝑥1 = 𝛥𝑡 𝑡2 − 𝑡1 Constant acceleration (more equations to solve) 𝑣𝑎𝑣𝑔 = 𝑣 = 𝑢 + 𝑎𝑡 1 𝑠 = 𝑢𝑡 + 𝑎𝑡 2 2 𝑣 2 = 𝑢 2 + 2𝑎𝑠 1 𝑠 = (𝑢 + 𝑣)𝑡 2 - Free Fall Acceleration - We refer to motion vertically, and replace acceleration with g, which is the magnitude of the free-fall acceleration 𝑔 = 9.8𝑚/𝑠 2 Vectors - Scalers only contain magnitude - Vectors have both magnitude and direction, and obey the rules of algebra - Components of a Vector - Components are given by: 𝑎𝑥 = 𝑎𝑐𝑜𝑠𝜃, and 𝑎𝑦 = 𝑎𝑠𝑖𝑛𝜃 - We can also find magnitude and orientation of vector a with: 𝑎 = √𝑎𝑥 2 + 𝑎𝑦 2 Kinematics in Two and Three Directions - Projectile Motion is the motion of a particle that is launched with an initial velocity - During its flight, the particle’s horizontal acceleration is 0, and it’s vertical acceleration is -g 𝑠𝑥 = (𝑢𝑐𝑜𝑠𝜃)𝑡 1 𝑠𝑦 = (𝑢𝑠𝑖𝑛𝜃)𝑡 − 𝑔𝑡 2 2 𝑣𝑦 = 𝑢𝑠𝑖𝑛𝜃 − 𝑔𝑡 - Uniform Circular Motion - If a particle travels along a circle or circular arc of radius r at constant speed v, it is in uniform circular motion and has an acceleration of constant magnitude - 𝑣2 𝑎= 𝑟 The direction of acceleration is towards the center of the circle or circular arc, and the acceleration is centripetal - T is the time for the particle to complete the circle, also called the period of revolution, or period 𝑇= - 2𝜋𝑟 𝑣 Relative Motion - When 2 frames of reference A and B are moving relative to each other at constant velocity, the velocity of particle P as measured by an observer in frame A usually differs from measured from frame B 𝑣𝑃𝐴 = 𝑣𝑃𝐵 + 𝑣𝐵𝐴 Force and Motion - Force is a vector quantity - Net force is the vector sum of all the forces acting on the body - Newton’s First Law - An object in motion stays in motion, and an object at rest stays at rest unless acted upon by an external, unbalanced force - Newton’s Second Law - The rate of change of momentum of a body is directly proportional to the force applied. - A free body diagram is a stripped down diagram in which only one body is considered, the external forces on the body are drawn - A gravitational force on a body is a pull by another body, usually the earth - 𝐹𝑔 = 𝑚𝑔 𝑊 = 𝑚𝑔 A normal force is the force on a body from the surface against which the body presses, always perpendicular to the surface - A Frictional force is the force on a body when the body slides along a surface, always parallel to the surface - Newton’s Third Law - If object A exerts a force FA on a object B, then B simultaneously exerts a equal but opposite force FB on A, - Friction - When a force tends to slide a body along a surface, a frictional force acts upon the body - - If the body does not slide, the frictional force is a static friction - If the body does slide, the frictional force is kinetic - The magnitude of 𝐹𝑠 has a maximum value, given by - 𝑓𝑠𝑚𝑎𝑥 = 𝜇𝑠 𝐹𝑁 Where 𝜇𝑠 is the coefficient of static friction - 𝑓𝑘 = 𝜇𝑘 𝐹𝑁 Where 𝜇𝑘 is the coefficient of kinetic friction Uniform Circular Motion - Net centripetal force 𝐹= 𝑚𝑣 2 𝑅 Work and Kinetic Energy - Kinetic Energy - 1 𝑚𝑣 2 2 Work is the energy transferred from an object from a force acting on the object - 𝑊 = 𝐹𝑑𝑐𝑜𝑠𝜃 For a particle, the change in kinetic energy equals the net work done on the particle - Spring force 𝐸𝑘 = - 𝐹𝑠 = −𝑘𝑥 (hooke’s law) - K is the spring constant, and x is the displacement of the spring - Work done by the spring - 1 2 𝑘𝑥 2 Power is the rate at which the force does work on an object 𝑊𝑠 = 𝑊 𝛥𝑡 P = Fv 𝑃𝑎𝑣𝑔 = Potential Energy and the Conservation of Energy - A force is a conservative force is the net work it does on a particle moving around any closed path, from an initial point and then back to the point is zero - Kinetic frictional force is a non conservative force - Potential energy is the energy that is associated in which a conservative force acts - Gravitational potential energy is the potential energy associated with a system consisting of the earth, and a nearby particle is the GPE 𝐸𝑝 = 𝑚𝑔ℎ - Where h is the height If there is a turning point where the particle reverses its motion, the kinetic energy is equal to 0 - Work done on an external force 𝑊 = 𝐸𝑘 + 𝐸𝑝 - Elastic Potential Energy 𝐸𝑃𝐸 = - Mechanical Energy 1 2 𝑘𝑥 2 𝐸𝑚𝑒𝑐 = 𝐸𝑘 + 𝐸𝑝 - Conservation of Energy - The total energy E of a system can only chance by amounts of energy that are transferred to or from the system - 1 1 𝑚𝑣 2 𝑖 + 𝑚𝑔ℎ𝑖 = 𝑚𝑣 2𝑓 + 𝑚𝑔ℎ𝑓 2 2 Where i is initial, and f is final Linear Momentum - p = mv - Impulse - 𝐽 = 𝐹𝑎𝑣𝑔 𝛥𝑡 𝛥𝑚 𝐹𝑎𝑣𝑔 = − 𝛥𝑣 𝛥𝑡 Conservation of Linear Momentum - If a system is isolated so that no net external force acts on it, the linear momentum of the system remains constant 𝑃𝑖 = 𝑃𝑓 - Inelastic Collision in One Dimension - In an inelastic collision of 2 bodies, the kinetic energy of the two-body system is not conserved - If the system is closed and isolated, the total linear momentum of the system must be conserved - 𝑃1𝑖 + 𝑃2𝑖 = 𝑃1𝑓 + 𝑃2𝑓 If the motion of the bodies is along a single axis and the collision is one dimensional: - 𝑚1 𝑣1𝑖 + 𝑚2 𝑣2𝑖 = 𝑚1 𝑣1𝑓 + 𝑚2 𝑣2𝑓 If the bodies stick together, the collision is completely inelastic collision and the bodies have the same final velocity - Elastic Collisions in One Dimension - A special type of collision in which the kinetic energy of a system of the colliding bodies is conserved - If system is closed and isolated, the linear momentum is also conserved Collisions in Two Dimensions - 𝑃1𝑖 + 𝑃2𝑖 = 𝑃1𝑓 + 𝑃2𝑓 If the collision is also elastic, 𝐾1𝑖 + 𝐾2𝑖 = 𝐾1𝑓 + 𝐾2𝑓 Rotation - Angular Position - To describe the rotation of a rigid body about a fixed axis, called the rotation axis, we assume there is a reference line in the body, perpendicular to the axis and rotating with the body 𝜃= - 𝑠 𝑟 1 revolution = 360° = 2𝜋rad - Angular Displacement - Angular Velocity and Speed 𝛥𝜃 = 𝜃2 − 𝜃1 - If a body rotates through an angular displacement in a time interval, its average angular velocity is 𝛥𝜃 𝛥𝑡 We use the right hand rule to see the direction of the velocity, thumbs up, facing 𝜔𝑎𝑣𝑔 = - the direction of the current, fingers facing direction of magnetic field - Another right hand rule is known as the fleming’s right hand rule when force is involved - Angular Acceleration 𝑎𝑎𝑣𝑔 = - 𝛥𝜔 𝛥𝑡 Work and Rotational Kinetic Energy - If the body rotates through an angle, the point moves along an arc with length s given by: 𝑠 = 𝜃𝑟 - The linear velocity of the point is tangent to the circle, and the point’s linear speed is given by: 𝑣 = 𝜔𝑟 - The linear acceleration of the point has both tangential and radial components, the tangential component is: 𝑎𝑡 = 𝛼𝑟 - The radial component is: 𝑎𝑟 = 𝜔2 𝑟 - If the point moves in uniform circular motion, the period T of the motion for the point and the body is: 𝑇 = 2𝜋 𝜔 Gravitation - The Law of Gravitation 𝐹=𝐺 - G = 6.67∗ 10−11 𝑁𝑚2 /𝑘𝑔2 𝑚1 𝑚2 𝑟2 Gravitational Potential Energy - The gravitational potential energy of a system of two particles with masses M and m separated by a distance of r - - GPE= − 𝐺𝑀𝑚 𝑟 Gravitational Acceleration 𝑎𝑔 = - Kepler’s Laws - The law of orbits - - All planets move in elliptical orbits with the sun at one focus The law of areas - A line joining any planet to the sun sweeps out equal areas in equal time intervals - 𝐺𝑀 𝑟2 The law of periods - The square of the period T of any planet is proportional to the cube of the semimajor axis a of its orbit 4𝜋 2 3 𝑇2 = ( )𝑟 𝐺𝑀 Oscillations - Frequency - - The frequency f is the number of oscillations per second, measured in hertz Period - The period T is the time required for one complete oscillation or cycle - 1 𝑓 Angular Frequency is related to the period and frequency of the motion by: 𝜔 = 2𝜋𝑓 - Linear Oscillator 𝑇= - A particle with mass m that moves under the influence of a Hooke’s law restoring force exhibits simple harmonic motion with - 𝜔 = √𝑚 - 𝑇 = 2𝜋√ (angular frequency) 𝑚 𝑘 (period) Pendulums - - 𝑘 - Simple Pendulum: 𝑇 = 2𝜋√𝐿/𝑔 Resonance - The velocity amplitude of the system is greatest in resonance Waves - Transverse and Longitudinal waves - Mechanical Waves can only exist in material media and are governed by Newton’s laws of motion - Transverse mechanical waves are waves in which it oscillates perpendicular to the waves direction of travel - Longitudinal waves oscillates parallel to the wave’s direction of travel Sinusoidal waves - y = 𝐴𝑠𝑖𝑛(𝑘𝑥 − 𝜔𝑡) *Notations may differ from textbook to textbook - Where A is the amplitude of the wave, k is the angular wave number, 𝜔is the angular frequency, and kx-𝜔𝑡is the phase - The wavelength is: 𝑘 = The wave speed is: 𝑣 = 2𝜋 𝜆 𝜔 𝑘 𝜆 = 𝑇 = 𝜆𝑓 Resonance - Standing waves on a string can be set up by a reflection of traveling waves from the ends of the string - If an end is fixed, it must be the position of a node - This limits the frequencies at which standing waves will occur on a given string - - Each possible frequency is a resonant frequency, and the corresponding standing wave pattern is an oscillation mode 𝑣 𝑣 𝑓= =𝑛 𝜆 2𝐿 Sound intensity - The intensity I of a sound wave at a surface is the average rate per unit area which energy is transferred by the wave through or onto the surface: 𝑃 𝐴 The intensity at a distance r from a point sources that emits sound waves of power 𝐼= - P is: 𝐼= - 𝑃 4𝜋𝑟 2 Doppler Effect - The doppler effect is a change in the observed frequency of a wave when the source or the detector moves relative to the transmitting medium 𝑣 ± 𝑣𝐷 𝑣 ± 𝑣𝑆 Where 𝑣𝐷 is the speed of the detector relative to the medium, and 𝑣𝑆 is that of the 𝑓′ = 𝑓 - sources - f’ tends to be greater for motion towards, and less for motion away Simple Harmonic Motion - - Occurs when something is in its equilibrium point - Force is proportional to displacement from equilibrium Frequency is the number of sound waves - Sound with single frequency is a pure tone - Under 20 Hz is infrasonic - Above 20 Hz is ultrasonic - The pitch is the brain’s interpretation of frequency - The pressure amplitude is the magnitude of maximum change in pressure measured relatively to undisturbed atmospheric pressure - Loudness is the amplitude of the wave Application in medicine - Ultrasounds, pulses, doppler flow meter - The sensitivity of the human ear - The principle of linear superposition - When 2 or more waves are present simultaneously at the same place, the resultant disturbance is the sum of the disturbance from the individual waves - Constructive and destructive interference of sound waves - Constructive interference is when 2 waves meet condensation-condensation or rare-rare - Destructive interference is when 2 waves meet rare-condensation Diffraction is the bending of waves around obstacles - Single slit- first medium - - - 𝜆 𝐷 Circular opening - - Sin 𝜃= 𝜆 Sin 𝜃 = 1.22 𝐷 Transverse Standing - Each pattern is a transverse wave pattern - Nodes = no vibration - Antinodes = maximum Superposition - When 2 or more waves are at the same place and collide and create a resulting wave z Temperature - Zeroth Law of Thermodynamics - If bodies A and B are each in thermal equilibrium with a third body C (the thermometer), then A and B are in thermal equilibrium with each other - The Kelvin Temperature Scale - - Standard SI unit, where the freezing point of water is 273.16 K Heat Capacity - If heat Q is absorbed by an object, the object’s temperature change is related by 𝑄 = 𝐶(𝑇𝑓 − 𝑇𝑖 ) where 𝑇𝑓 is the final temperature and𝑇𝑖 is the initial temperature - If object has mass m, then 𝑄 = 𝑐𝑚(𝑇𝑓 − 𝑇𝑖 ) - Celsius and Fahrenheit Scales - The celsius temperature scale is defined by: 𝐹𝑐 = 𝑇 − 273.15 - - T is in kelvins 9 Fahrenheit temperature is defined by: 𝑇𝑓 = 𝑇𝑐 + 32 5 Radiation - Radiation is an energy transfer via the emission of electromagnetic energy - 𝑃𝑟𝑎𝑑 = 𝜎𝜖𝐴𝑇 4 Everything with temperature gives us thermal radiation - Above absolute zero is vibrational energy 𝑄/𝑡 = 𝑝𝑜𝑤𝑒𝑟 = 𝜖𝜎𝐴𝑇 4 The Kinetic Theory of Gases - Average translational kinetic energy per particle 𝐾𝐸 = - Internal Energy of a Monatomic ideal gas 𝑈= - 3 𝑘𝑇 2 3 𝑛𝑅𝑇 2 The distribution of molecular speeds - Particles travel at different speeds, but it's possible to have an average particle speed - Avogadro’s Number - One Mole of a substance contains 𝑁𝐴 elementary units 𝑁𝐴 = 6.02 ∗ 1023 𝑚𝑜𝑙 −1 - Ideal Gas - pV = nRT - Can also be written as pV = NkT 𝑅 Where k, the boltzmann constant, is 𝑘 = 𝑁 = 1.38 ∗ 10−23 𝐽/𝐾 - 𝐴 The number of moles n contained in a sample of mass consisting of N molecules is given by: 𝑛 = 𝑁 𝑁𝐴 = 𝑀𝑠𝑎𝑚 𝑀 = 𝑀𝑠𝑎𝑚 𝑚𝑁𝐴 Coulomb’s Law - Conductors - - Materials in which a significant number of electrons are free to move Coulomb’s Law describes the electrostatic force between two charged particles 1 𝑞1 𝑞2 = 2 4𝜋𝜖0 𝑟 Where 𝜖0 is the permittivity constant 𝐹= - Conservation of Charge - The net electric charge of any isolated system is always conserved - Like charges repel, opposites attract - Charged objects can be created by friction Electric Fields and Electric Forces - Like mass, electric charge is an intrinsic property 𝑒 = 1.6 ∗ 10−19 𝐶 - Law of conservation of electric charge - During any process, the net electric charge of an isolated system remains constant - Conductors and Insulators - Conductors are substances that readily conduct - - Insulators are materials that conduct charge poorly - - Ex. metal Ex. plastic, rubber Charging by contact and induction - Contact is directly touching - Induction is charging without physical contact 𝐸= - 𝐹 𝑞0 Electric Field Lines - Help visualize the direction and magnitude of electric fields - The field vector at any point is tangent to a field line through that point - The density of field lines in any region is proportional to the magnitude of the electric field in that region - From positive charges to negative charges - Field due to a point charge - 1 𝑞 = 2 4𝜋𝜖0 𝑟 Force on a point charge in an electric field 𝐸= 𝐹 = 𝑞𝐸 Electric Potential Energy and Electric Potential - The electric potential v at a given is the EPE of a small test charge q situated at that point divided by the charge itself 𝐸𝑃𝐸 𝑞 Relation between charge and potential difference for a capacitor 𝑣= - - Magnitude q of the charge on each plate of a capacitor is directly proportional to the magnitude v of the potential difference between places 𝑞 = 𝑐𝑉 - The electric potential difference - 𝐹 = 𝑞0 𝐸is the electric force - The work depends on charge 𝑞0 - 𝑊𝐴𝐵 𝐸𝑃𝐸𝐴 𝐸𝑃𝐸𝐵 = − 𝑞0 𝑞0 𝑞0 A positive charge accelerates from a region of higher EPE towards a region of lower EPE - 1 electron volt is the amount by which the potential energy of an electron changes when the electron moves through the potential difference of 1 volt - 1𝑒𝑉 = 1.60 ∗ 10−19 𝐽 The EP difference created by point charges 𝑘𝑞𝑞0 𝑘𝑞𝑞0 − 𝑟𝐴 𝑟𝐵 → −𝑊𝐴𝐵 𝑘𝑞 𝑘𝑞 𝑉𝐵 − 𝑉𝐴 = = − 𝑞) 𝑟𝐵 𝑟𝐴 𝑊𝐴𝐵 = 𝑘𝑞 - Potential of a point charge 𝑣 = - When 2 or more charges are present, the potential due to all the charges is 𝑟 obtained by adding together the individual potentials - Equipotential surfaces and their relation to the electric field - An equipotential surface is a surface where EP is the same everywhere - The net force does 0 work as charge moves on the equipotential surface - EF is everywhere perpendicular to associated equipotential surfaces and points in the direction of the decreasing potential - Capacitors and Dielectrics - A capacitor: 2 or more conductors, no physical contact - Dielectric: Electrically insulating material - Dielectric constant 𝑘 = 𝐸0 𝐸 Electric Currents - Electromotive force and current - The mas potential difference is the electromotive force (EMF) - Flow of chart = electric current - 𝛥𝑞 𝛥𝑡 If the charge moves in the same direction, the current is direct current - If the charge mores in 1 direction, then switches directions, it’s in an alternating 𝐼= current - The conventional current is a hypothetical flow of positive charges that would have the same effect in a circuit as the movement of negative charges - Ohm’s Law - - - Current is in Ampere A - Voltage is in Volts V - Resistance is in Ohms 𝛺 Electric Power - - Resistance = voltage / current The power is equal to the current multiplied by the voltage Alternating current 𝑃= - 𝑣2 𝑅 Series Writing - Devices are connected in a way so that there is same electric current in each device - 𝑉 = 𝑉1 + 𝑉2 = 𝐼𝑅1 + 𝐼𝑅2 = 𝐼(𝑅1 + 𝑅2 ) = 𝑅𝑠 𝑅𝑠 =equivalent resistance - Series resistor = 𝑅𝑆 = 𝑅1 + 𝑅2 . .. - Parallel writing - Devices are connected so that voltage is the same 𝐼 𝑅𝑝 1 1 1 = + . .. 𝑅𝑝 𝑅1 𝑅2 𝐼=𝑉 - Kirchhoff’s rules - Junction rule - At any junction in the electrical circuit, the sum of the currents flowing into the junction is equal to the sum of the currents flowing out of the junction - Loop rule - Around closed circuit loop, the sum of the potential drop is the sum of the potential rise Magnetic Fields - North magnetic pole vs south magnetic pole, opposites attract and likes repel - The force that a magnetic field exerts on a moving charge - The charge must be moving - Velocity must have component that is perpendicular to direction of the magnetic field - The motion charged particle in a field - Charged particle is perpendicular to the field - Magnetic force is perpendicular to the velocity and directed towards center 𝑚𝑣 𝑟= 𝑞𝐵 Electromagnetic Waves - The oscillating current I in the antenna wires create magnetic field B at point P that is tangent to the circle centered on the wires - The field is directed into the page when the current is upward and out of the page when the current is downwards - As oscillating current changes, the magnetic field changes accordingly - An electromagnetic field wave is transverse - Can travel through a vacuum or material substance - All waves move through vacuum at speed c, which is the speed of light in a vacuum - - 𝑐 = 3.00 ∗ 108 m/s Electromagnetic spectrum - Lower frequency waves generally produced by electric oscillator circuits - Higher frequency waves are generated using electron tubes called klystrons - The energy carried by electromagnetic waves - A measure of the energy stored in the electric field E of an electromagnetic wave is provided by the electromagnetic identity - As electromagnetic waves move through space, it carries energy - The intensity - S is the electromagnetic intensity - 𝑃 𝐴 The volume of space which the wave passes is ctA - The total energy in the volume is 𝑆 = 𝑆= - 𝑐 𝜇0 𝐵2 Polarization - Electromagnetic waves are transverse waves, so they can be polarized - Wave is linearly polarized - - Vibrations always occur in one direction - This direction is called the direction of polarization Malus’ law - Once light has been polarized with a piece of polarizing material, it’s possible to use a second piece to change polarization direction and to adjust to the intensity of light 𝑆 = 𝑆0 𝑐𝑜𝑠 2 𝜃 The Refraction of Light, Lenses, and Other Optical Instruments - The index of refraction - Change in speed as ray of light goes from 1 material to another - Causes ray to deviate from the “incident direction” - This change is called refraction 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑣𝑎𝑐𝑢𝑢𝑚 𝑐 = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑣 Snell’s law and the refraction of light 𝑛= - - When light travels from material with refractive index 𝑛1 into a material with refractive index 𝑛2 , the refractive ray, the incident ray, and the normal to the interface all lie in the same plane 𝑛1 𝑠𝑖𝑛𝜃1 = 𝑛2 𝑠𝑖𝑛𝜃2 - Apparent Depth - - An object underwater appears closer than it actually is 𝑛2 𝑑′ = 𝑑 𝑛1 - Where d’ is the apparent depth, d is the actual depth Total internal reflection - When the angle of incident reaches a certain value, its critical angle is an angle of refraction, 90 degrees - The total internal reflection occurs only when light travels from higher to lower medium index - - Critical angle: 𝑠𝑖𝑛𝜃𝑐 = 𝑛2 𝑛1 Polarization and the reflection and refraction of light - For incident angles other than 0 , unpolarized light becomes partially polarized in reflecting from a nonmetallic surface such as water - There is 1 special angle where reflected light is completely polarized parallel to the surface and the reflected ray is only partially polarized: Brewster’s angle 𝜃𝐵 - - Tan 𝜃𝐵 = 𝑛2 𝑛1 The spreading of light into color components is dispersion