Exam II Review

Review of traveling wave interference Phase changes due to: Optical path length differences sources out of phase General solution

Single slit diffraction – E-field integration across entire slit to point a screen (path length differences cause interference pattern) Short cut to find destructive interference pattern (divide slit up into ‘2m’ and consider pairs of rays summed up over entire slit) Rayleigh’s criteria (optical resolution limit) – minimum of diffraction pattern produced by object 1

Ideal double slit interference pattern (a~wavelength  2 point sources) Diffraction grating – constructive interference condition Actual double slit interference pattern (a wavelength) – Convolution of ideal double slit and single slit patterns

Actual double slit interference pattern (a wavelength) – Convolution of ideal double slit and single slit patterns

Fresnel Coefficients:

Interference in thin films dielectrics

Dielectrics Antireflection Coatings

Michelson Interferometer

Law of reflection: Snell’s law: Critical angle and Total internal reflection:

Image formation from flat mirror and flat refractive boundaries: Dispersion Image from refractive spherical surface and ray tracing:

Thin spherical lenses with ray tracing:

Thin Lens – Ray tracing

Spherical reflectors with ray tracing:

Compound lenses: Image of first lens becomes object of second lens Camera: Zoom lenses, f/#, exposure, depth of field

Optics of the Eye: Near point and Far point Farsightedness (hyperopia) and Nearsightedness (myopia) Corrective lenses, Power of lens = 1/f, diopter = 1/m

Angular magnification of eyepieces

NA of microscope objective

Telescope

Spatial resolution of microscope (same as lens!) Rayleigh’s criteria for lens same as aperture:

1.Electrons, neutrons, atoms, etc. exhibit the properties of interference and diffraction. 2. The wavelength of matter waves is related to momentum: 3. E&M radiation can be thought of as composed of photons, or ‘wave packets’. Matter can be though of as composed of wave packets as well. 4. The energy of a photon is related to it’s (average) frequency: 5. Particles which are confined to a small box form standing waves --- only discrete amounts of momentum and energy are allowed.

Bragg condition: Constructive interference X-ray Diffraction by Crystal – Bragg Condition

Matter wave confined --- Review of standing waves Chapter 21

Matter wave confined --- particle in a box

Hydrogen atom confines the electron to some region of space. This produces the Energy levels of the atoms and ultimately explains the discrete spectrums of the atoms. The confinement area changes with KE of particle, so solutions differ from simple particle in a box:

Spectroscopy --- The Discrete Hydrogen spectrum