Page 34 - Modern Optical Engineering The Design of Optical Systems

Optics Overview 17

seems to require for its explanation that light behaves as if it consisted
of particles.
In brief, when short-wavelength light strikes a photoelectric material,
it can knock electrons out of the material. As stated, this effect could
be explained by the energy of the light waves exciting an electron suffi-
ciently for it to break loose. However, when the nature of the incident
radiation is modified, the characteristics of the emitted electrons
change in an unexpected way. As the intensity of the light is increased,
the number of electrons is increased just as might be expected. If the
wavelength is increased, however, the maximum velocity of the electrons
emitted is reduced; if the wavelength is increased beyond a certain value
(this value is characteristic of the particular photoelectric material
used), the maximum velocity drops to zero and no electrons are emitted,
regardless of the intensity. The energy of a photon in electron volts is
given by 1.24 divided by the wavelength in micrometers (microns).
Thus the energy necessary to break loose an electron is not stored
up until enough is available (as one would expect of the wavelike
behavior of light). The situation here is more analogous to a shower of
particles, some of which have enough energy to break an electron
loose from the forces which bind it in place. Thus the particles of
shorter wavelength have sufficient energy to release an electron. If
the intensity of light is increased, the number of electrons released is
increased and their velocity remains unchanged. The longer-wavelength
particles do not have enough energy to knock electrons loose, and
when the intensity of the long-wavelength light is increased, the
effect is to increase the number of particles striking the surface, but
each particle is still insufficiently powerful to release an electron from
its bonds.
The apparent contradiction between the wave and particle behavior of
light can be resolved by assuming that every “particle” has a wavelength
associated with it which is inversely proportional to its momentum. This
has proved true experimentally for electrons, protons, ions, atoms, and
molecules; for example, an electron accelerated by an electric field of a
few hundred volts has a wavelength of a few angstroms (10 4 m) asso-
ciated with it. Reference to Fig. 1.1 indicates that this wavelength is
characteristic of x-rays, and indeed, electrons of this wavelength are
diffracted in the same patterns (by crystal lattices) as are x-rays.

Bibliography
Born, M., and E. Wolf, Principles of Optics, Cambridge, England, Cambridge University
Press, 1997.
Brown, E., Modern Optics, New York, Reinhold, 1965.
Ditchburn, R., Light, New York, Wiley-Interscience, 1963.
Drude, P., Theory of Optics, New York, Dover, 1959.