Appendix A
Optical Limit of Maxwell’s Equations
From a long view of the history of mankind the most significant
event of the nineteenth century will be judged as Maxwell’s
discovery of the laws of electrodynamics.
— Richard Feynman
A.1 The Eikonal
Optics is a study of visible light and the application of visible light in instruments which enhance images and communications. Optical instruments rely on
the behavior of electromagnetic waves in the visible range of wavelengths (400–
700 nm) passing through regions and instruments which have sizes much larger
than the wavelength of the light. Under these circumstances, wave interference and
diffraction are too small an effect to notice. However, viewing very small objects
invokes wavelength limits on image resolution.
As Maxwell’s theory of electromagnetism is complete, the ‘laws of optics’
are derivable from Maxwell’s equations in the short wavelength limit. Start with
Maxwell’s equations in the form
∇ · (E) = 4πρ f
∇ × E = −
1
c
∂B
∂t
∇ · B = 0
∇ ×
1
μ
B
=
4π
c
J f +
1
c
∂ (E)
∂t
.
The subscript f indicates that the corresponding quantities are for free charge and
current densities, not bound ones.
© Springer Nature Switzerland AG 2020
W. C. Parke, Biophysics, https://doi.org/10.1007/978-3-030-44146-3
627
Optical Limit of Maxwell’s Equations
From a long view of the history of mankind the most significant
event of the nineteenth century will be judged as Maxwell’s
discovery of the laws of electrodynamics.
— Richard Feynman
A.1 The Eikonal
Optics is a study of visible light and the application of visible light in instruments which enhance images and communications. Optical instruments rely on
the behavior of electromagnetic waves in the visible range of wavelengths (400–
700 nm) passing through regions and instruments which have sizes much larger
than the wavelength of the light. Under these circumstances, wave interference and
diffraction are too small an effect to notice. However, viewing very small objects
invokes wavelength limits on image resolution.
As Maxwell’s theory of electromagnetism is complete, the ‘laws of optics’
are derivable from Maxwell’s equations in the short wavelength limit. Start with
Maxwell’s equations in the form
∇ · (E) = 4πρ f
∇ × E = −
1
c
∂B
∂t
∇ · B = 0
∇ ×
1
μ
B
=
4π
c
J f +
1
c
∂ (E)
∂t
.
The subscript f indicates that the corresponding quantities are for free charge and
current densities, not bound ones.
© Springer Nature Switzerland AG 2020
W. C. Parke, Biophysics, https://doi.org/10.1007/978-3-030-44146-3
627