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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