Interference and Storage
What limits how much we can store
on CD-ROM
Interference of Waves
Amax
 If crests match
crests, then waves
Amax
interfere
constructively
 Crests will match 2Amax
if waves are one
wavelength, two
wavelengths, …
apart: path
difference = ml
wave 1
wave 2
sum
Destructive Interference
 If crests match troughs Amax
(180° out of phase),
then waves interfere
Amax
destructively
 Crests will match
troughs if waves are
one/half wavelength,
three/half wavelengths,
… apart: path
difference = (m+½)l
wave 1
wave 2
sum
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 = Emax2/(2cm0)
 Constructive interference produces brighter light;
destructive interference produces dimmer light.
Comparing Interference
2Emax
Emax
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
Direction of
wave motion
l
a
Wave Crest
Wave Trough
l = wavelength
a = aperture width
The Double Slit Experiment
 Waves spreading out from two points, such as
waves passing through two slits, will interfere
l
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
l
a
Wave crest
Wave trough
Spot of
constructive
interference
Spot of
destructive
interference
Single Slit Math
y
b
a
q
tan q = y/D
D
a/2 q b
Path length difference = a/2 sin q
Diffraction Math
 The locations of successive minima are given by
a
1

sin q   m  l (m  0,  1,  2,...)
2
2

a sin q  nl (n  1,  2,  3.....)
 tan q = y/D
 for small angles, sin q ~ q ~ tan q = y/D
Diffraction by a circular aperture
 A circular aperture of diameter d
l
sin q  1.22 (1st minimum)
d
 Single slit of width a
sin q 
l
a
(1st minimum)
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)
1.22l 1.22l
  sin

d
d
1
R
 As before, q approximately y/L
Comments on Resolvability
y
1.22 l
 
D
d
R
 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
devices