34.5 - Diffraction
Diffraction: The expansion or spreading of a
wave front.
In this section, we switch from light to sound waves to discuss the important
phenomenon of diffraction. We briefly switch to sound waves because they provide a
way to describe diffraction using an everyday experience.
In Concept 1, we show the diffraction of wave fronts of a sound wave as they pass
through a doorway. Only a section of each wave front can pass through the doorway. If
this section of the wave front did not expand, it would move straight along the gray path.
Instead, it expands spherically after passing through the doorway. The spherical
expansion of the sound wave allows the person in the picture to hear the sound.
When you hear a friend down the hallway calling you, even though she is out of your
line of sight, you hear her in part because the sound waves diffract as they emerge from
the doorway. For a given size opening, waves of longer wavelength diffract more than
those of shorter wavelength. Because light has a much shorter wavelength than sound,
it would spread out far less after it passed through the doorway. This is why you can
hear the voice of your friend, even when you cannot see her. However, even though
you cannot observe light diffraction for doorway-sized openings, scientists have long
observed it for smaller openings.
The debate over the cause of diffraction created a tale of considerable irony. The story
starts with a competition sponsored by the French Academy on the subject of
diffraction. The Frenchman Augustin Jean Fresnel (1788 - 1827) submitted a paper to
the judges in 1818 discussing diffraction that was premised on considering light as a
wave.
A noted mathematician, Simeon-Denis Poisson, had earlier mocked Fresnel’s theories,
pointing out that Fresnel’s theory predicted that the shadow of a circular opaque object
subjected to a bright light would exhibit a bright spot in its center. Since the circular
object blocks the center portion of a screen from the light source, this result is highly
surprising.
Noted mathematicians can be wrong (or should trust their mathematics). The
Fresnel/Poisson debate was resolved by experiment. In Concept 2, the reddish image
on the screen was created by shining a bright light at a small ball bearing. You can see
the expected bright light surrounding the circumference of the ball, but í surprise! í
there is also a bright spot at the center of the shadow caused by light diffracting around
the ball’s perimeter.
Fresnel was right, and Poisson unintentionally helped to confirm his theory. The irony is
that though Fresnel did all the work, and Poisson initially ridiculed the theory, the bright
center today is often called the Poisson spot. Others call it the Fresnel spot, perhaps a
more appropriate name, with Arago spot yet another name (François Arago was the
judge of the competition).
Waves also expand around sharp edges into regions that would otherwise be in shadow
if the wave traveled only in a straight line. This type of diffraction causes an interference
pattern. The photograph in Concept 3 shows straight-edge diffraction. Light from a point source passes by a sharp, well defined edge, and the
resulting diffraction causes a pattern on a screen behind the object.
Diffraction
Wave fronts “expanding”
Poisson spot
Bright spot caused by diffraction
Straight-edge diffraction
Causes interference pattern
34.6 - Huygens’ principle
The Dutch scientist Christian Huygens (1629 - 1695) concluded that light was a wave,
made up of tiny points that emit spherical wavelets like the ones you see in Concept 1
to the right. Although his model has its limitations, it provided a basis for explaining
many phenomena that scientists observed, and his model was usefully employed and
expanded. Here we explain his fundamental principle, and show how his model can be
used to explain diffraction.
As Huygens wrote:
...each particle of matter in which a wave spreads, ought not to communicate its
motion only to the next particle which is in the straight line drawn from the
luminous point, but that it also imparts some of it necessarily to all the others
which touch it and which oppose themselves to its movement. So it arises that
around each particle there is made a wave of which that particle is the center.