Superposition Interference Diffraction

• Wavelength


  The shortest distance between two peaks/troughs in a sine wave
• Wavelength


  • long wavelength light
  • medium wavelength light
  • short wavelength light
• Frequency


  The number of cycles in a second
• Phase


  A particular point in time on the cycle of a waveform, measured as an angle in degrees
• Phase relationships


  • In phase (0 or 360° apart)
  • Out of phase (peaks and troughs occur at different time points)
  • Completely out of phase (180° apart)
• Phase difference


  The amount the waves are out of phase
• Interference


  The variation of wave amplitude that occurs when waves of the same or different frequency come together
• Interference


  • Constructive interference (peaks/troughs occur at same time points, amplitude is sum of both)
  • Destructive interference (peaks/troughs occur at different time points, amplitude is sum of both)
• For constructive interference to occur, the path difference between the two waves must be 0, λ, 2λ,..., nλ
• For destructive interference to occur, the path difference between the two waves must be 0.5λ, 1.5λ,..., (n + 0.5λ)
• Interference can occur for more than one light wave, but the resulting waveform still results from the sum of all of the waves
• Superposition


  The resulting waveform from the sum of multiple waves
• Coherent


  Two light waves have the same waveform, phase difference and wavelength
• Generally, light is incoherent as it consists of a number of different wavelengths, frequencies and amplitudes
• Lasers are coherent light sources
• Coherence


  The degree to which a light source has the same wavelength, frequency and phase
• Coherence characteristics


  • Wide bandwidth = low degree of coherence (more than one wavelength)
  • Narrow bandwidth = high degree of coherence (a single wavelength)
• Light sources


  • Spectral light sources (e.g. sodium/mercury lamps) - low coherence, wide bandwidth
  • Lasers - high coherence, narrow bandwidth
• Michelson Interferometer


  Light is split into two beams using a beam splitter, the beams only differ by path length, changing the mirror distance changes the path length and alters the interference pattern
• Optical Coherence Tomography (OCT)


  Uses interference to measure distances
• Wavefronts


  Every point on a primary wavefront serves as the source of a following wavefront, the new wavefront is the "envelope" of these newly generated wavefronts
• Diffraction


  The bending of waves around the corners of an obstacle or aperture into the region of the geometrical shadow of the obstacle
• Diffraction occurs for all wave forms - sound, water and electromagnetic spectrum. It can only be explained by the wave theory of light
• Diffraction


  • Slit width larger than wavelength: the wave passes through unchanged
  • Slit width equal to, or smaller than wavelength: diffraction occurs
• Interference of the diffracted waveform produces a light pattern (on a screen) of varying intensity
• Single Slit Diffraction


  Constructive interference occurs where waves travel the same distance, destructive interference occurs where waves travel different distances
• Double Slit Diffraction


  Constructive interference occurs where path difference is nλ, destructive interference occurs where path difference is (n*1/2)λ
• For double slit diffraction, fringes form from a combination of interference (from the waves passing through both slits) and diffraction (from the light passing through each individual slit)
• Diffraction gratings consist of multiple slits (hundreds per mm) and the resulting fringe pattern is much sharper than one generated by a single or double slit
• Diffraction gratings


  Can be used to build a spectrometer which enables us to analyse the spectral content of a light source and the atomic source(s) of light emission
• Even if an optical system is free from spherical and chromatic aberration, the resolution of the system is limited by its aperture size due to diffraction
• Resolving Power


  The minimum distance of separation required to resolve two objects
• Rayleigh Criterion


  Two diffraction images are defined to be resolved when the first/ central maximum of one Airy disc coincides with the first order minimum of the second Airy disc
• The "dip" in light intensity between the two peaks is about 26% and this difference can just be resolved by the human eye