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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
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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’sLaw • 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 components
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 Change in internal energy Energy flowing out Work done inside
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 betweenthe 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
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
