1. A Brief History of Light
Two main theories of Light: does it consist of waves or
of particles?
Wave Theory
Particle (Corpuscular) Theory
Christian Huygens
( 1629 – 1695 )
Isaac Newton
( 1642 – 1727 )

2. Do they explain observed phenomena?
(1) Rectilinear Propagation (Production of shadows)
Particle theory easily explains; wave theory explains by saying that
waves don’t bend around corners (diffract) because they are
traveling too fast for diffraction to be observed

3. Can theory
explain
Wave Theory
Particle Theory
Propagation
yes
yes

4. (2) Reflection From a Barrier
easily explained by
both theories

5. Can theory
explain
Wave Theory
Particle Theory
Propagation
yes
yes
Reflection
yes
yes

6. (3) Refraction
Explainable by both theories; for
particle theory, light must speed
up in denser medium (like sound);
for wave theory, light must slow
down in denser medium (like water);
not testable in 1600’s

7. Can theory
explain
Wave Theory
Particle Theory
Propagation
yes
yes
Reflection
yes
yes
Refraction
yes
yes

8. 1801: Thomas Young discovered
2-Pt. interference of light:
observed series of light
and dark bands on
distant screen
Passed light through 2 narrow slits

9. According to particle theory,
should see only two bands
of light
Easily explainable by wave theory
using path-length-difference and
interference arguments

10. Can theory
explain
Wave Theory
Particle Theory
Propagation
yes
yes
Reflection
yes
yes
Refraction
yes
yes
2-Pt.
Interference
yes no

11. 2-Pt. Interference of Light
2 sources separated by a distance d
1st order bright fringe x S1
central bright
fringe d L S2
Screen is located a distance L away from sources
1st order bright fringe is a distance x away from central
bright fringe

12. 2-Pt. Interference of Light
2 sources separated by a distance d
1st order bright fringe x S1 d L S2 T λ
Light travels 1λ farther from S2 than from S1, so it arrives in
phase and produces a bright fringe

13. 2-Pt. Interference of Light
2 sources separated by a distance d
1st order bright fringe θ x S1 d L S2 T λ
∟S1TS2 approximates a right angle, especially when L >> d
opp λ
If so, then sin θ = =
hyp d

14. 2-Pt. Interference of Light
By similar triangles, ∟SQR is equal to ∟S2S1T S
1st order bright fringe θ x S1 θ d Q R L S2 T λ
opp x
then tan θ = =
adj L

15. For small angles, sin θ = tan θ
1st order bright fringe θ x S1 θ d Q R L S2 T λ λ x
sin θ =
tan θ = d L ~
For small angles, sin θ = tan θ d λ x d
x d ~ =
λ = d L L

16. (4) Diffraction
Pass light through small single slit
on a distant screen:
Pass laser light through small hole:

17. Unexplainable by particle theory
Explainable by wave theory using Huygen’s Principle
(each source on a wavefront acts as its own source of
circular waves, the leading edge of which forms the
wavefront)
Light passes through slit;
points A, A’, B, B’, C, C’ act as sources;
A and A’ interfere, sometimes constructively
and sometimes destructively A B C A’
Likewise B and B’; and C and C’ B’ C’
All places of constructive int. match up,
as do places of destructive int.

18. Can theory
explain
Wave Theory
Particle Theory
Propagation
yes
yes
Reflection
yes
yes
Refraction
yes
yes
2-Pt.
Interference
yes no
Diffraction
yes no

19. Maxwell’s Equations proved that light was a
James Clerk Maxwell
( 1831 – 1879 )
James Clerk Maxwell
proved that light was a
transverse, sinusoidal wave

20. Photoelectric Effect discovered in 1887 by Heinrich Hertz
The emission of electrons from a metallic
surface when illuminated by
electromagnetic radiation
Heinrich Hertz
( 1857 – 1894 )

21. Shine red light on metallic surface; no emission for low intensity
The energy of a wave
depends on its amplitude,
so by increasing the
intensity, we should get
emission
metallic
surface
metallic
surface
But no emission occurred, even for high intensities

22. Instead of increasing intensity, it was found that by increasing the
frequency, there was a point at which there was photoemission,
even for very low intensities
This threshold frequency was the same every time the experiment
was done, for that metal; differed for different metals e-
metallic
surface
Photoelectrons came off metal
with a certain KE
KE can be measured by applying a reverse potential, to pull
electrons back ( a “stopping voltage”)

23. Increasing the intensity of the light caused more photoelectrons to
metallic
surface
Increasing the intensity of the light
caused more photoelectrons to
be emitted e-
metallic
surface e- e-
But the same stopping voltage brought all of the electrons,
back, indicating that all of them had the same KE

24. It was found that the way to increase the KE of the photoelectrons was
to increase not the intensity of the light but the frequency
Even at low intensity, photoelectrons
were emitted with a large KE e-
metallic
surface
A larger stopping voltage was required to stop photoemission
Again, increasing the intensity
caused more photoelectrons, but
their KE remained the same
(same stopping voltage) e-
metallic
surface e- e-

25. Formally:
(1) Low-frequency light (red) did not emit electrons,
even at high intensities (bright light)
(2) Above a certain threshold frequency, emission began
immediately, even at low intensities
(3) If frequency is held constant and intensity is increased, the number
of photoelectrons increases, but their KE remain the same (same
stopping voltage is required)
(4) As the frequency increases, the kinetic energy of the
photoelectrons increases also (greater stopping voltage is
required)
Not explainable by current theory of light (as a wave)

26. Einstein’s explanation of the Photoelectric Effect (1905):
(drawn from work done by Max Planck with black-body radiators)
- the energy of light is carried in discrete units, call “quanta”
(singular: quantum), or “photons”
the energy of light is directly proportional to the frequency
of the light
E = energy
f = frequency
h = Planck’s constant
E = h f
= x J s

27. ex. A photon of red light has a wavelength of 6.83 x 10-7 m.
(a) Determine the frequency of a photon of red light.
v = f λ
c = f λ
λ λ c
3 x 108 m/s
f = =
= f = x 1014 Hz λ
6.83 x 10-7 m
(b) Determine the energy of a photon of red light.
E = h f
h = x J s
E = ( 6.63 x J s)( 4.39 x 1014 Hz )
E = x J

28. So the energy of a photon of red light is 2.91 x 10-19 J
What is the combined energy of two photons of red light?
2 ( 2.91 x J ) = x J
so the energy of light is not continuous;
can be this
can have 2 photons
but cannot be this
can’t have 1.5 photons
can have 1 photon
energy can be this
Difference between them is a “quantum step”
“quantum leap?”

29. Einstein’s explanation of the Photoelectric Effect (1905):
(drawn from work done by Max Planck with black-body radiators)
- the energy of light is carried in discrete units, call “quanta”
(singular: quantum), or “photons”
the energy of light is directly proportional to the frequency
of the light
E = energy
f = frequency
h = Planck’s constant
E = h f
= x J s
increasing the intensity of light increases the number of
photons, but not their energies

30. Summary of findings:
(1) Low-frequency light (red) did not emit electrons,
even at high intensities (bright light)
(2) Above a certain threshold frequency, emission began
immediately, even at low intensities
(3) If frequency is held constant and intensity is increased, the number
of photoelectrons increases, but their KE remain the same (same
stopping voltage is required)
(4) As the frequency increases, the kinetic energy of the
photoelectrons increases also (greater stopping voltage is
required)

31. (1) Low-frequency light (red) did not emit electrons,
even at high intensities (bright light)
Einstein:
Electrons are held within a metal by a certain
amount of energy ( a work function ) that must be
overcome in order for the electrons to be emitted
work function: energy that holds electrons within a metal
Photons of red light do not have energy to overcome
the work function; electrons are “jiggled” but not
ejected

32. (2) Above a certain threshold frequency, emission began
immediately, even at low intensities
Einstein:
At the threshold frequency, the photons have just enough energy to overcome the work function
One photon will cause one electron to be ejected
Since all of the energy of the photon was used to overcome the work function, the KE of the photoelectrons = 0
Above the threshold frequency, there is some leftover
energy that goes into KE of the photoelectrons
KE = ( Energy of the light) - ( work function )

33. Energy of photons can
both supply the energy
needed to overcome the
work function and give
the photoelectrons
kinetic energy
( Energy of the light ) = ( work function ) + KE
h f = ϕ + KE

34. (3) If frequency is held constant and intensity is increased, the number
of photoelectrons increases, but their KE remain the same (same
stopping voltage is required)
Einstein:
Increasing the intensity of the light increases the
number of photons, but not their energies
One photon causes one photoelectron, so more
photons result in more photoelectrons emitted
Frequency (and energy) of light is constant, so KE
of photoelectrons (leftover energy from that needed
to overcome the work function) remains constant
h f = ϕ + KE
KE = h f - ϕ = constant

35. (4) As the frequency increases, the kinetic energy of the
photoelectrons increases also (greater stopping voltage is
required)
Einstein:
Increasing the frequency of the light increases its
energy
Work function of metal is constant, so leftover
energy for KE increases as the energy of the
light increases
h f = ϕ + KE
KE = h f - ϕ
increases
increases
constant
So by treating light as a particle, with energy equal to hf,
the photoelectric effect was easily explained

36. Can theory
explain
Wave Theory
Particle Theory
Propagation
yes
yes
Reflection
yes
yes
Refraction
yes
yes
2-Pt.
Interference
yes no
Diffraction
yes no
Photoelectric
Effect no
yes

37. So is light a wave or a particle?
Can be either
Wave-Particle Duality:
Light can exhibit properties of either waves or particles, depending on the phenomenon observed
Light is never both a wave and a particle
within the same experiment
Before observing light (with an experiment), light is in
some indeterminate state
Analogy with Schrodinger’s cat

38. Cat in box with vial of poison and radioactive
source; if source decays, lever breaks vial, cat dies;
if source does not decay, cat is alive
Erwin Schrodinger
( 1887 – 1961 )
To find out if cat is alive, must open the box; before opening, cat
is in the indeterminate state; is either dead or alive (can’t be both)
Opening box will force cat into one of two states (dead or alive)

39. Similarly, before observing light, it is the indeterminate state
of being either a wave or a particle
Observe it with an experiment
If we observe it by passing it
through 2 narrow slits, it assumes
wave properties
interference pattern
If we observe it by shining it on a
metallic surface, it assumes
particle characteristics

40. Emission Spectra
Observed in the 1880’s; not understood

41. Rutherford’s Atom ( from Gold-Foil Experiment )
Positive charge in atom concentrated at its center (nucleus);
negative charge orbits the nucleus
Question: Since positive and negative charges attract each other,
why don’t the electrons spiral into the nucleus?
Neils Bohr: There must be places
of stability where the
electrons do not spiral in +
Why?
not sure

42. The Bohr Atom Different orbitals have different energies
; electrons can move between levels
; when they move down to a lower level, they emit a photon of precise energy, the difference in energies of
the levels

43. Explains emission spectra; energies of lines correspond to
difference in energies between orbitals

46. Doppler Redshift