Exam 2 Review23-1 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.23-2,3 Magnetic Flux and Faraday’s Law of Induction23-4 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…23-5 Mechanical Work and Electrical Energy Induced EMF23-6 Generators and Motors Motor Generator23-7 Inductance23-8,9 RL Circuits and Energy Stored in Magnetic Field23-10 Transformers Can be used to change voltage supply….25-1 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…25-2 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 receding25-3 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…25-4 Energy and Momentum in Electromagnetic Waves • Electric and magnetic field energy densities are equal in EM wave. – Given by: Intensity: Momentum:25-Polarization • Polarization refers to direction of oscillating electric field…26-1 The Reflection of Light The law of reflection states that the angle of incidence equals the angle of reflection:26-2 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.26-3 Spherical Mirrors26-4 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.26-5 The Refraction of Light (n > 1 for media) θ1 θ2 Reflected light is polarized26-6 Ray Tracing for Lenses Concave lens.. Convex lens.. Principle the same as for mirrors..26-7 The Thin-Lens Equation In thin-lens approximation, we can relate distance via focal length..26-8 Dispersion and the Rainbow28-1 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…28-1 Superposition and Interference • For 2 light sources which are monochromatic and coherent, these are conditions for interference: - m is an integer (0, ±1, ±2, etc…)28-2 Young’s Two-Slit Experiment Constructive interference Destructive interference28-3 Interference in Reflected Waves Constructive interference Destructive interference Conditions for interference change due to phase changes28-3 Interference in Reflected Waves • Reflection with film involve: - Phase change - Wavelength change • Changes the condition for interference once more… Constructive interference Destructive interference n is index of refraction in film….28-4 Diffraction Destructive interference m = +1 m = +2 m = -1 m = -2 • Diffraction involves the spreading of waves through a cavity/barrier - Sound waves will diffract around doors, corners, and other barriers.28-5 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… - Rayleighʼs law on resolution… θ angle of first fringe… Both sources of light pass through an aperture e.g. the eye, microscope…28-6 Diffraction Gratings The 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