9.5 Introduction to the dipole force 195
Glass prism
Incident light
Refracted light
Fig. 9.10Radiation that is deflected
by a glass prism (or a mirror) exerts a
force on that object equal and opposite
to the rate of change of momentum of
the radiation.
Laser beam
Gaussian distribution
of light intensity
Atom
B
B
A
A
Fig. 9.11The refraction of light by a
dielectric sphere with a refractive in-
dex greater than that of the surround-
ing medium. In a laser beam with a
Gaussian profile the intensity along ray
A is greater than for ray B. This leads
to a resultant force on the sphere to-
wards the region of high intensity (cen-
tre of the laser beam), in addition to
an axial force pushing in the direction
of the beam. Analogous forces arise on
smaller particles such as atoms. After
Ashkin (1997).
These simple considerations show that the forces associated with ab-
sorption and refraction by an object have similar magnitude but they
have different characteristics; this can be seen by considering a small
dielectric sphere that acts as a converging lens with a short focal length,
as shown in Fig. 9.11. In a laser beam of non-uniform intensity, the
difference in the intensity of the light refracted on opposite sides of the
sphere leads to a resultant force that depends on the gradient of the
intensity: a sphere with a refractive index greater than the surrounding
medium,nsphere>nmedium, feels a force in the direction of increasing
intensity, whereas a sphere withnsphere<nmediumis pushed away from
the region of high intensity.^33 Thus the sign of thisgradient force(also^33 The calculation of this force using ge-
ometrical optics is straightforward in
principle, but integration over all the
different rays and inclusion of reflection
coefficients makes it complicated.
known as the dipole force) depends onnsphere. The refractive index
of materials varies with frequency in the characteristic way shown in
Fig. 9.12. This behaviour can be understood in terms of a simple classi-