Exam 9: Wave Optics

-Wave optics is concerned with phenomena that cannot be adequately explained by geometric (ray) optics. -These phenomena include: Interference, Diffraction, Polarization -Interference refers to the interaction of two waves passing through the same region of space at the same time. -Constructive interference: amplitudes of waves add the waves are in phase -Destructive interference: amplitudes of waves subtract the waves are out of phase -The wave character of light is also very useful in describing diffraction (bending of waves around the edges of an opening or an obstacle). Note that diffraction is observed only when the obstacle is on the order/smaller than the wavelength of light. -Light (electromagnetic radiation in general) is a transverse wave. A transverse wave can be represented in several ways. The direction of propagation is perpendicular to the wavefronts (or wave crests) and is represented by an arrow (ray). -Young’s double-slit experiment: This experiment shows that light is a wave, because it undergoes wave interference. Outcome: if light from the same source passes through two closely spaced and narrow slits, many lines (instead of two) can be seen behind the slit. This result can be explained by the wave interference phenomenon: the light waves leaving the slits spread out (diffraction) and interfere with each other (interference). -Except for the zeroth-order fringe at the center, the position of the fringes depends on wavelength. If white light falls on the slits, the central fringe is white, but the higher-order fringes contain a spectrum of colors. -An interference pattern similar to the double-slit experiments obtained when light passes through a large number of evenly spaced parallel slits, called a diffraction grating. The peaks of constructive interference (principal/primary maxima) are much sharper and brighter for a diffraction grating than for a two-slit device. -Diffraction by a single slit: When using different sources of monochromatic light, the greater the wavelength, the wider the fringes. When using an adjustable slit, making the slit narrower makes the fringes wider. The width of the central bright fringe (maximum) is equal to the distance between the positions of zero intensity on both sides of the central bright fringe. -Double-slit vs. single-slit interference: A double slit interference pattern has equally spaced maxima (that gradually decrease in strength) and minima. A single slit interference pattern has a broad intense central band flanked by a series of narrower, less intense, secondary maxima and a series of minima and Can’t say exactly where bright fringes are located, except for the brightest one at θ = 0. -Rayleigh criterion: Two images are just resolvable when the center of the diffraction disk of one image is directly over the first minimum in the diffraction pattern of the other. Well resolved: middle doesn’t overlap and not resolved: just has one center. -Angle: This is the limit on resolution set by the wave nature of light due to diffraction. -A smaller angle means higher resolution: smaller/closer objects can be resolved -Quantum mechanics: Energy is not continuous but can have only particular discrete values. Light has particle-like properties – it is made of quanta (particles) called photons. At the same time, light also has wave-like properties – thus the wave-particle duality. Wave-particle duality applies to all matter (electrons, protons, etc.) -Thermal radiation = energy radiated by objects in the form of electromagnetic waves. It is generated by the thermal motion of charged particles in matter -Planck's quantum hypothesis: In this model, an oscillator having a frequency (emitting and absorbing EM radiation of frequency) can have its energy increase or decrease only in discrete steps of size hf (called the quantum of energy) - the energy is quantized. -Atomic spectra: EM emissions of hot gases due to electrons transitioning between energy levels in individual atoms and molecules. Atomic spectra are quantized/discrete: only certain wavelengths/frequencies, are emitted. -The photoelectric effect The setup consists of a photocell - an evacuated tube with a metal plate (E) and a collector wire (C) that are connected by a voltage source. When light (or other EM radiation) shines on the metallic plate, there is a current in the circuit. This indicates that electrons are ejected from the metal plate E and are moving towards the collector wire C.: Experimental fact: when light strikes materials, it can eject electrons from them. -Of the energy provided by light, electrons use some to break free from the metal (binding energy: BE). The rest appears as kinetic energy of the electrons -No electrons are emitted if the frequency of the light is below a cutoff frequency f0, no matter how intense the light (how much light there is). -For f