2.1 The Nature of Light
39
so that E lies along the negative x axis as Fig. 2.5 shows. At a later time, say t =
π/2ω, the electric field vector has rotated through 90° and now lies along the positive
y axis at z ref . Thus as the wave moves toward the observer with increasing time, the
resultant electric field vector E rotates clockwise at an angular frequency ω. It makes
one complete rotation as the wave advances through one wavelength. Such a light
wave is right circularly polarized.
If one chooses the negative sign for δ, then the electric field vector is given by
E = E 0
e x cos(ωt − kz) + e y sin(ωt − kz)
(2.13)
Now E rotates counterclockwise and the wave is left circularly polarized.
2.1.4 Quantum Aspects of Light
The wave theory of light adequately accounts for all phenomena involving the transmission of light. However, in dealing with the interaction of light and matter, such as
occurs in dispersion and in the emission and absorption of light, neither the particle
theory nor the wave theory of light is appropriate. Instead, one must turn to quantum
theory, which indicates that optical radiation has particle as well as wave properties.
The particle nature arises from the observation that light energy is always emitted or
absorbed in discrete units called quanta or photons. In all experiments used to show
the existence of photons, the photon energy is found to depend only on the frequency
v. This frequency, in turn, must be measured by observing a wave property of light.
As described in Sect. 1.2.1 and illustrated in Fig. 1.2, the physical properties of
a photon can be measured in terms of its wavelength, energy, or frequency. The
relationship between the energy E and the frequency v of a photon is given by
E = hv
(2.14)
where h = 6.6256 × 10
–34 J·s is Planck’s constant. When light is incident on an atom,
a photon can transfer its energy to an electron within this atom, thereby exciting it
to a higher energy level. In this process either all or none of the photon energy is
imparted to the electron. The energy absorbed by the electron must be exactly equal
to that required to excite the electron to a higher energy level. Conversely, an electron
in an excited state can drop to a lower state separated from it by an energy hv by
emitting a photon of exactly this energy.
Drill Problem 2.1 Using Eq. (2.14), show that the corresponding wavelengths
of photons with energies of 0.95 eV and 0.80 eV are 1310 nm and 1550 nm,
respectively.
39
so that E lies along the negative x axis as Fig. 2.5 shows. At a later time, say t =
π/2ω, the electric field vector has rotated through 90° and now lies along the positive
y axis at z ref . Thus as the wave moves toward the observer with increasing time, the
resultant electric field vector E rotates clockwise at an angular frequency ω. It makes
one complete rotation as the wave advances through one wavelength. Such a light
wave is right circularly polarized.
If one chooses the negative sign for δ, then the electric field vector is given by
E = E 0
e x cos(ωt − kz) + e y sin(ωt − kz)
(2.13)
Now E rotates counterclockwise and the wave is left circularly polarized.
2.1.4 Quantum Aspects of Light
The wave theory of light adequately accounts for all phenomena involving the transmission of light. However, in dealing with the interaction of light and matter, such as
occurs in dispersion and in the emission and absorption of light, neither the particle
theory nor the wave theory of light is appropriate. Instead, one must turn to quantum
theory, which indicates that optical radiation has particle as well as wave properties.
The particle nature arises from the observation that light energy is always emitted or
absorbed in discrete units called quanta or photons. In all experiments used to show
the existence of photons, the photon energy is found to depend only on the frequency
v. This frequency, in turn, must be measured by observing a wave property of light.
As described in Sect. 1.2.1 and illustrated in Fig. 1.2, the physical properties of
a photon can be measured in terms of its wavelength, energy, or frequency. The
relationship between the energy E and the frequency v of a photon is given by
E = hv
(2.14)
where h = 6.6256 × 10
–34 J·s is Planck’s constant. When light is incident on an atom,
a photon can transfer its energy to an electron within this atom, thereby exciting it
to a higher energy level. In this process either all or none of the photon energy is
imparted to the electron. The energy absorbed by the electron must be exactly equal
to that required to excite the electron to a higher energy level. Conversely, an electron
in an excited state can drop to a lower state separated from it by an energy hv by
emitting a photon of exactly this energy.
Drill Problem 2.1 Using Eq. (2.14), show that the corresponding wavelengths
of photons with energies of 0.95 eV and 0.80 eV are 1310 nm and 1550 nm,
respectively.