Introduction to Nanotechnology

7.7. FERRQFLUlOS 191
FerroRuids can also form mapctic field tunable diffnction gratings. Difiction
is the result of interference of two or more light waves of the same wavelength
traveling paths of slightly different lengths before arriving nt a detector such as :I
photographic film. When the pathlcngth differs by halr a wavelength, the wilves
destructivcly interfere, resulting in a tltirk band on the film. When the path lengths
difler by a wnvelengh, then the wavcs constnictively interfcrc, producing a bright
band on thc lilm. A diffraction grating consists of small slits separated by distances
of the order of the wave!ength of thc incident light. We saw above that when a DC
magnetic field of sufficient strength is applied perpendicular to ii magnetofluid film,
an equilibrium two-dimensional hexagonal lattice is formed with columns of
nanoparticles accirpyhg the lattice sitcs. This structure can act as 6 two-dimensional
optical diffraction grating that diffracts incoining visible light. Figure 7.28 shows a
black and white picture of the chromntic (colored) rings of light and darkness
resulting from thc di ffmction and interFcrcncc when a focused pamllcl beam of white
light is passed through I magnetic fluid film that has a rnagnctic field applied
perpendicular to it. The diffraction pattcrn IS determined 'by rhc equation
d sin 0 = a;. (7.6)
where d is the disrancc between the chains of nonoparticles, 0 is thc angle between
!he outgoing light and thc direction normal to the film, n is an integer, and j. is the
wavelength of the light, We saw earlier that [he distance between the chains d
Figure 7.28. Chromatic rings resulting from the diffraction and interference of a k am of white
light indent on a fernfluid lilm in a perpendtcular DC applied magnetic lield. [With permission
from H. E. Hornig et al., J. Phys. Chem. So/,ds 62, 1749 (2001).]