Waves, Light

1
Waves, Light Quanta
Tim Freegarde
Web Gallery of Art National Gallery, London
2
Huygens wave construction

• place secondary sources along wavefront

Christiaan Huygens (1629-1695)

• ...and trigger when wavefront arrives

• apply to sinusoidal waves by taking into account
  the phase with which components arrive

• combine by adding the amplitudes

• contributions may therefore interfere
  constructively or destructively

3
Huygens wave construction

• Fresnel integral

• phasors shorter / rotate more quickly at distance
  to give spiral

4
Aragos bright spot

• M A Fresnel, La diffraction de la lumière (1818)

• S D Poisson

Let parallel light impinge on an opaque disk, the
surrounding being perfectly transparent. The disk
casts a shadow - of course - but the very centre
of the shadow will be bright. Succinctly, there
is no darkness anywhere along the central
perpendicular behind an opaque disk (except
immediately behind the disk).

• F Arago

One of your commissioners, M Poisson, had deduced
from the integrals reported by Fresnel the
singular result that the centre of the shadow of
an opaque circular screen must, when the rays
penetrate there at incidences which are only a
little more oblique, be just as illuminated as if
the screen did not exist. The consequence has
been submitted to the test of direct experiment,
and observation has perfectly confirmed the
calculation.
5
Youngs double slit diffraction
x
6
Youngs double slit diffraction
x
amplitude
intensity
7
Single slit diffraction
x
8
Single slit diffraction
amplitude
x
intensity
9
Diffraction grating
x

• place secondary sources along wavefront

• ...and trigger when wavefront arrives

• apply to sinusoidal waves by taking into account
  the phase with which components arrive

INTERFERENCE

• combine by adding the amplitudes

• contributions may therefore interfere
  constructively or destructively

10
Complex numbers
Im
r
Re