Interference and Storage
What limits how much we can store
on CD-ROM
Interference of Waves
Amax
If crests match wave 1
crests, then waves
interfere Amax
wave 2
constructively
Crests will match 2Amax
if waves are one sum
wavelength, two
wavelengths, …
apart: path
difference = ml
Destructive Interference
If crests match troughs Amax
(180° out of phase), wave 1
then waves interfere Amax
destructively wave 2
Crests will match
troughs if waves are
one/half wavelength, sum
three/half wavelengths,
… apart: path
difference = (m+½)l
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 Double amplitude Zero amplitude
of electric field of electric field of electric field
yields medium yields quadruple yields zero
intensity light intensity (very intensity (no)
bright) light light
Diffraction
Waves spread out, or diffract as they pass through
a slit
Direction of
l
wave motion
Wave Crest
a 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 Wave crest
Wave trough
Spot of
d 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 Wave crest
Wave trough
Spot of
a 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
l
sin q (1st minimum)
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)
1.22l 1.22l
sin
R
1
d d
As before, q approximately y/L
Comments on Resolvability
y 1.22 l
R
D d
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