Physics 361
Principles of Modern Physics
Lecture 5
Photons and Electromagnetic
Waves
• Light has a dual nature. It exhibits both wave
and particle characteristics
– Applies to all electromagnetic radiation
– Different frequencies allow one or the other
characteristic to be more easily observed
• The photoelectric effect and Compton scattering
offer evidence for the particle nature of light
– When light and matter interact, light behaves as if it
were composed of particles
• Interference and diffraction offer evidence of the
wave nature of light
Wave Properties of Particles
• In 1924, Louis de Broglie postulated that
because photons have wave and particle
characteristics, perhaps all forms of matter
have both properties
• Furthermore, the frequency and wavelength of
matter waves can be determined
de Broglie Wavelength and
Frequency
• The de Broglie wavelength of a particle is
h
l=
p
• The frequency of matter waves is
E
ƒ
h
Dual Nature of Matter
• The de Broglie equations show the dual
nature of matter
• Each contains matter concepts
– Energy and momentum
• Each contains wave concepts
– Wavelength and frequency
Suggested in 1924, Measured in
1926 and 1927
• Both experiments performed electron diffraction off a
crystal lattice (Davisson, Germer, and Thompson)
The Electron Microscope
• The electron microscope
depends on the wave
characteristics of electrons
• Microscopes can only resolve
details that are slightly smaller
than the wavelength of the
radiation used to illuminate the
object
• The electrons can be
accelerated to high energies
and have small wavelengths
Example: Find the de Broglie wavelength of
a 1500-kg car whose speed is 30 m/s.
Solution: The car’s wavelength is
l=h/mv=6.63x10-34 J•s/(1.5x103)(30m/s)
= 1.5x10-38 m
Example: Find the de Broglie wavelength of
a 1500-kg car whose speed is 30 m/s.
Solution: The car’s wavelength is
l=h/mv=6.63x10-34 J•s/(1.5x103)(30m/s)
= 1.5x10-38 m
The wavelength is so small compared to the
car’s dimension that no wave behavior is
to be expected.
Example: Compare the de Broglie wavelength of 54-eV electrons
with spacing of atomic planes in a crystal, which is 0.91x10-10 m.
Solution: KE of a 54-eV electron is
KE=(54eV)(1.6x10-19 J/eV)=8.6x10-18 J
KE=1/2 mv2, mv=(2mKE)1/2
l=h/mv=h/(2mKE)1/2=1.7x10-10 m
Comparable to the spacing of the atomic planes, so diffraction occurs
m=9x10-31kg
h=6.63x10-34Js
What are the matter waves made up of?
(Waves of what?)
Compare to electromagnetic waves.
In the case of photons, electricity and
magnetism tell us the waves are spatial
variations in the electric and magnetic
fields.
Detectors will measure an intensity
proportional to the |amplitude|2 of the E&M
wave.
Average power per unit area 
2
2
Emax Bmax
Emax
c Bmax
I 


2 o
2 o c
2 o
Since we know energy is
delivered by discrete photons,
the detector must just be
measuring the number of
photons arriving per unit time.
Since photons all travel the
same speed, this is the same
as saying the number per
unit length.
Intensity of matter waves measure number per unit
length.
Matter waves vary in space and are some
function of position.
y (x)
y (x)
Their |amplitude|2 is also proportional to
number of particles per unit length
measured by a detector, as with photons.
y (x)
2
This also applies to infinitesimal slices in
space.
But for a finite-magnitude particle wave,
this would imply zero particles in the slice!
The y (x) is telling us the
2
probability to find a particle in
that slice of space.
These wave magnitudes are
just proportional to probability
to find a particle in that region.
This is actually the same for
photons as well.
To understand matter waves and the basics of
quantum mechanics, we will explore simple
interference effects (two slit interference)
Let’s first understand a single slit pattern
• A single slit placed between a distant light source and a screen
produces a diffraction pattern
– It will have a broad, intense central band
– The central band will be flanked by a series of narrower, less
intense secondary bands
• Called secondary maxima
– The central band will also be flanked by a series of dark
bands
• Called minima
Single Slit Diffraction
• According to Huygen’s
principle, each portion of
the slit acts as a source of
waves
• The light from one portion
of the slit can interfere with
light from another portion
• The resultant intensity on
the screen depends on the
direction θ
Single Slit Diffraction, 2
• All the waves that originate
at the slit are in phase
• Wave 1 travels farther than
wave 3 by an amount equal
to the path difference (a/2)
sin θ
• If this path difference is
exactly half of a
wavelength, the two waves
cancel each other and
destructive interference
results
Single Slit Diffraction, 3
• In general, by extending
this trick, we can find that
destructive interference
occurs for a single slit of
width a when sin θdark = mλ
/a
– m = 1, 2, 3, …
• Doesn’t give any
information about the
variations in intensity along
the screen
Single Slit Diffraction, 4
• The general features of the
intensity distribution are
shown
• A broad central bright fringe
is flanked by much weaker
bright fringes alternating
with dark fringes
• The points of constructive
interference lie
approximately halfway
between the dark fringes
Example of LASER
light double-slit
diffraction
• The dotted blue line is due to single slit diffraction
• The red solid line is due to the interference between slits
Single slit

Double slit

sin θdark = mλ / a
sin θbright = mλ / d
m = 1, 2, 3, …
m =0 1, 2, 3, …
19
d>>a