1Exam 2 ReviewDr. Anthony Timmins223-1 Induced Electromotive Force!• EMF can be induced in second circuit if current in the first is changing – When current in the first is stable, 0 EMF in the second – Magnitude of the induced current is proportional to the rate at which the magnetic field is changing.323-2,3 Magnetic Flux and Faraday’s Law of Induction423-4 Lenz’s Law!• An induced current always flows in a direction that opposes the change that caused it. • If magnetic field faces one direction • Magnetic field created by the induced current will be the opposite direction…523-5 Mechanical Work and Electrical Energy!Induced EMF623-6 Generators and MotorsMotor Generator723-7 Inductance823-8,9 RL Circuits and Energy Stored in Magnetic Field923-10 TransformersCan be used to change voltage supply1025-1 The Production of Electromagnetic Waves• Electromagnetic waves (EM) are produced by oscillating charges. • Electric (E) and Magnetic (B) fields oscillate perpendicular to each other. • Both oscillate perpendicular to the direction of propagation.1125-2 The Propagation of Electromagnetic Waves• All EM waves in vacuum propagate at same speed… – Move more slowly in medium.• Doppler effect occurs when waves reflect from object+ sign for approaching- sign for receding1225-3 The Electromagnetic Spectrum•In vacuum, relation between frequency (f) and wavelength (λ) given by:The full range of frequencies of electromagnetic waves is called the electromagnetic spectrum,1325-4 Energy and Momentum in Electromagnetic Waves• Electric and magnetic field energy densities are equal in EM wave. Given by:Intensity: Momentum:1425-Polarization• Polarization refers to direction of oscillating electric field.1526-1 The Reflection of LightThe law of reflection states that the angle of incidence equals the angle of reflection:1626-2 Forming Images with a Plane Mirror• Mirror image is upright, but appears reversed right to left. • Mirror image appears to be the same distance behind the mirror that the object is in front of the mirror. • Mirror image is the same size as the object.1726-3 Spherical Mirrors1826-4 Ray Tracing and the Mirror Equation•P ray reflects (projects) through the focal point •F ray reflects (projects) parallel to the axis… • (C ray) reflects back along its incoming path.do : distance from the mirror to the object di : distance from the mirror to the image f : focal length.1926-5 The Refraction of Light(n > 1 for media)θ1θ2Reflected light is polarized2026-6 Ray Tracing for LensesConcave lens.Convex lens.Principle the same as for mirrors.2126-7 The Thin-Lens EquationIn thin-lens approximation, we can relate distance via focal length.2226-8 Dispersion and the Rainbow2328-1 Superposition and Interference• Interference will be constructive where the two waves are in phase (b) • Destructive where they are out of phase (c)Superposition just means one can add two waves to get the total wave.2428-1 Superposition and InterferenceFor 2 light sources which are monochromatic and coherent, these are conditions for interference: m is an integer (0, ±1, ±2, etc)2528-2 Young’s Two-Slit ExperimentConstructive interferenceDestructive interference2628-3 Interference in Reflected WavesConstructive interferenceDestructive interferenceConditions for interference change due to phase changes2728-3 Interference in Reflected Waves• Reflection with film involve: - Phase change - Wavelength change • Changes the condition for interference once more…Constructive interferenceDestructive interferencen is index of refraction in film.2828-4 DiffractionDestructive interferencem = +1m = +2m = -1m = -2•Diffraction involves the spreading of waves through a cavity/barrier -Sound waves will diffract around doors, corners, and other barriers.2928-5 Resolution• Diffraction through a small circular aperture results in a circular pattern of fringes.. • If two sources have overlapping first fringes, they cannot be resolved… - Rayleigh’s law on resolution…θ angle of first fringe…Both sources of light pass through an aperture e.g. the eye, microscope…3028-6 Diffraction GratingsThe condition for constructive interference in a diffraction grating:• System with a large number of slits is called a diffraction grating. • Crystals can act as a diffraction grating • Help determine the wavelength of X rays passing
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