Waves, Light & QuantaTim 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

Arago’s bright spot

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

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).

• S D Poisson:

• 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

Young’s double slit diffraction

x

s

a

6

Young’s double slit diffraction

x

s

amplitude

intensity

d

d2

da

7

Single slit diffraction

x

y

s

a

8

Single slit diffraction

x

s

amplitude

intensity

aa2

aa2

y

a

9

Diffraction grating

x

d

y

s

a

• place secondary sources along wavefront

• ...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

INTERFERENCE

10

Complex numbers

sincossincos ii sincos i

dsincos i sincos ii

sincosd

di sincos ii Re

Im

r

cosr

sinr sincos ir ire z

cos ii ee 2

1

sin ii eei

2

1