Direct Energy, 2018a

102 6.2 The Wave and Particle Natures of Light
small chunk, of light. A related quantityis a phonon, which is a quanta,
or small chunk, of lattice vibrations. We will discuss phonons in a later
section, and theydo not relate to light. Although, phonons can perturb
light, and that is the basis for acousto-optic devices. The second wayto
understand light is to think of it as a wave with a wavelength λ measured
in nm. White light has a broad bandwidth while the light produced bya
laser has a verynarrow bandwidth.
These two descriptions of light complement each other. A photon is the
smallest unit of light, and it has a particular wavelength. The energyof a
photon of light with wavelength λ is given by
E = hf = hc
λ . (6.1)
The quantity h is called the Planck constant, and it has a tinyvalue,
h =6.626 · 10 −34 J · s. The quantity c is the speed of light in free space,
c =2.998 · 10 8 m s .
In SI units, energyis measured in joules. However, other units are sometimes
used byoptical engineers because the energyof an individual photon
is tinycompared to a joule. Another unit that is used is the electronvolt,
or eV. The magnitude of the charge of an electron is q =1.602 · 10 −19 C.
The electronvolt is the energyacquired bya charge of this magnitude in
the presence of a voltage dierence of one volt [68, p. 8]. Energyin joules
and energyin eV are related bya factor of q.
E [J]
= q · E [ eV]
(6.2)
Equations 6.1 and 6.2 can be combined to relate the energyof a photon in
eV and the corresponding wavelength in nm.
1240
λ [nm]
= E [ eV] . (6.3)
Sometimes, energyis specied in the unit of wave number, cm −1 , which
represents the reciprocal of the wavelength of the corresponding photon.
Energyin joules and energyin wave number are related by
E [ J] = hc
λ
E [ J] = 6.626 · 10−34 J · s · 2.998 · 10 8 m s
λ [cm]
· 100 cm m
(6.4)
(6.5)
E [ J] =1.986 · 10−23 E [ cm −1 ] . (6.6)