Interference and Storage What limits how much we can store on CD-ROM

Interference of Waves  If crests match crests, then waves interfere constructively  Crests will match if waves are one wavelength, two wavelengths, … apart: path difference = m A max 2A max wave 1 wave 2 sum A max

Destructive Interference  If crests match troughs (180° out of phase), then waves interfere destructively  Crests will match troughs if waves are one/half wavelength, three/half wavelengths, … apart: path difference = (m+½) wave 1 wave 2 sum A max

What This Means for Light  Light is electromagnetic radiation  A light wave is oscillating electric and magnetic fields  The amplitude of the oscillation represents the maximum electric (or magnetic) field and determines the intensity of light  Intensity depends on the square of the maximum electric field: I = E max 2 /(2c  0 )  Constructive interference produces brighter light; destructive interference produces dimmer light.

Comparing Interference E max 2E max Medium amplitude of electric field yields medium intensity light Double amplitude of electric field yields quadruple intensity (very bright) light Zero amplitude of electric field yields zero intensity (no) light

Diffraction  Waves spread out, or diffract as they pass through a slit  = wavelength a = aperture width a Direction of wave motion Wave Crest Wave Trough

The Double Slit Experiment  Waves spreading out from two points, such as waves passing through two slits, will interfere d Wave crest Wave trough Spot of constructive interference Spot of destructive interference

Diffraction Patterns  Light traveling through a single slit also creates a pattern, due to interference between wavefronts passing through different regions of the slit a Wave crest Wave trough Spot of constructive interference Spot of destructive interference

Single Slit Math Path length difference = a/2 sin  a  y D  b a/2 tan  = y/D b

Diffraction Math  The locations of successive minima are given by  tan  = y/D  for small angles, sin  ~  ~ tan  = y/D

Diffraction by a circular aperture  A circular aperture of diameter d  Single slit of width a

Do the Activity, Continuing through it After finishing Diffraction Pattern of a Red Laser, first two or three groups should jump to Green Laser part, then give green lasers to other groups when done

Resolvability  Two objects are just resolved when the central diffraction maximum of one object is at the first minimum of the other. (Rayleigh’s criterion)  As before,  approximately y/L

Comments on Resolvability  If want to resolve objects closer to each other (smaller y), need smaller wavelength of light or larger aperature  This is called the diffraction limit

Why Do We Care? CD-ROMS and other optical storage devicesCD-ROMS