PHYS 241 Final Exam Review

Kevin Ralphs

Overview

• General Exam Strategies• Concepts• Practice Problems

General Exam Strategies

• Don’t panic!!!• If you are stuck, move on to a different

problem to build confidence and momentum• “Play” around with the problem• Take fifteen to twenty minutes before the

exam to relax… no studying.• Dimensional analysis is a good tool, but can

give false results

Concepts

• Inductance• AC Circuits– RMS– Reactance– Impedance– Phasors

• Displacement Current• Electromagnetic Waves (Light)– Wave/Particle Duality– Poynting Vector

Concepts

• Optics– Refraction• Index of Refraction• Snell’s Law

– Total Internal Reflection

– Malus’s Law– Mirrors– Lenses– Diffraction

Inductance

• What does it tell me?– The flux through a loop is proportional to the

currents on conductors in the vicinity (including itself)

– This is a direct consequence of the principle of superposition and magnetic fields being proportional to the currents that create them

Inductance

• Why should I care?– This is the sister component to the capacitor making it one

of the most fundamental electronic componentsCapacitor Inductor

Depends on geometry and material between the plates

Depends on geometry and material in intervening space

Proportionality between charge and voltage

Proportionality between flux and current

Stores energy in an electric field Stores energy in a magnetic field

Causes current to lag voltage Causes current to lead voltage

Current starts at maximum and drops to zero

Current starts at zero and increases to maximum

Alternating Current (AC) - RMS

• What does it tell me?– RMS is a type of averaging– First square the wave form, then we average and

take the square root• Why should I care?– This allows us to keep a form of the Joule heating

law

AC - Reactance

• What does it tell me?– Capacitors and inductors resist changes in the state of

the circuit – Reactance is a measure of this• Why should I care?

– Calculating the voltages on capacitors and inductors in an AC circuit can be complicated

– Reactance give you a direct link between the average voltage across these components and the RMS current in an Ohm’s law type format

– It also shows how the frequency of the applied voltage affects the system

AC - Impedance

• What does it tell me?– It represents the relationship (magnitude and

phase difference) between the applied voltage and the current

• Why should I care?– Impedance provides a compact way to carry a lot

of information about your circuit

AC - Impedance

• Since the impedance carries phase information, it is a complex number

• The circuit is at resonance when the impedance is a real number– This corresponds to maximum power transfer to

the resistors

AC - Phasors

• A phasor is a graphical representation of the relationship between voltage and current in a system

• This exploits the power of complex numbers as both vectors and rotations

• The phasor rotates through the complex plane and the real projections of the phasor give the measured value

• See Demonstration

Displacement Current

• What does it tell me?– A changing electric field produces a magnetic field

as if there was a current flowing that is proportional to the change in flux

Displacement Current

• Why do I care?– The correction completes Ampere’s law bringing it

in agreement with the Biot-Savart Law– Like Faraday’s law, this allows for the propagation

of electromagnetic waves

Poynting Vector

• What does it tell me?– Energy and momentum can be carried away by

electromagnetic waves

Work done insideEnergy flowing outChange in internalenergy

Poynting Vector

• Why do I care?– It is a conservation law– Newton’s third law fails without it– Hints at the need for special relativity– The intensity (power) of light is defined as the

time average of the vectors magnitude

– Radiation pressure is related to the intensity

Index of Refraction

• What does it tell me?– The ratio of the speed of a wave in a reference

medium (we choose the vacuum) and another medium

• Why should I care?– The index of refraction influences nearly all optical

phenomena in some way• Depends on electrical and magnetic properties of

the medium – sensitive to frequency (i.e. )

Snell’s Law

• What does it tell me?– The relationship between

the indices of refraction andthe angles of refraction andreflection

• Why should I care?– This concept is the “building block” for more advanced

concepts such as thin film diffraction• Remember that ALL angles are measured from the

NORMAL of the surface

Malus’s Law

• What does it tell me?– How the intensity of polarized light is affected by a

polarizer

– Your book defines theta to be the angle between the transmission axes of two polarizers

– Alternatively, it is the angle between the plane of polarization and the transmission axis of the polarizer

– If the light is unpolarized, the intensity if halved

Assumptions/Conventions

• Wavelength of light is much shorter than the length scale of the geometry– Treat light as rays; i.e. no bending

• Small angle deviations from the optical axis– Spherical surface is nearly parabolic

• The biggest challenge in applying the formulae is following the correct sign convention

MirrorsRules for Ray Diagrams

Parallel Rays Reflected through focal point

Focal Rays Reflected parallel to optical axis

Radial Rays Reflected back on itself

Sign Convention

s is positive if object is on the incident-light side

s’ is positive if the image is on the reflected-light side

R is positive if the mirror is concave

LensesRules for Ray Diagrams

Parallel Rays Refracted through focal point

Focal Rays Refracted parallel to optical axis

Central Rays No deflection when refracted

Sign Convention

s is positive if object is on the incident-light side

s’ is positive if the image is on the refracted-light side

r is positive if center of curvature is on the refracted-light side

Diffraction

• What does it tell me?– How a wave behaves near objects– Only an appreciable affect when the length scale

of the wave and the geometry are similar• Visible light: 400nm – 700nm• Sound waves: 17mm – 17m

Interference

• What does it tell me?– How waves mix together– Based on the principal of superposition

– Always occurs, but is especially noticeable when the waves are coherent

Interference

• There are two main sources of interference that we will consider– Path length difference

– Reflected waves can pick up a phase shift when going into a medium with a higher index of refraction

Main Strategy

• For any kind of diffraction, the game is always about counting up phase shifts; these can be expressed in terms of angles or wavelengths– Angles

• Constructive Interference: Even multiples of π• Destructive Interference: Odd multiples of π

– Wavelengths• Constructive Interference: Integer multiples of λ• Destructive Interference: Odd half-integer multiples of λ

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