Chapter 3 – Making Light Work in Biology  91

where nw and ng refer to the refractive indices of water (~1.33) and glass (~1.515, for com­

monly used BK7 low-​fluorescence borosilicate glass), respectively, which indicates a critical

angle of ~61°. These refractive index values relate to the wavelength-​dependent dispersion

relation of light, and across the VIS light spectrum of 400–​700 nm result in a range of 1.344–​

1.342 (nw) and 1.529–​1.514 (ng). The simplest empirical model for the dispersion relation is

embodied in the Cauchy equation:

(3.38)

n

c

c

c

c

c

λ

λ

λ

λ

( ) =

+

+

+

≈

+

0

2

2

4

4

0

2

2



The agreement with experiment in the VIS range is very good (within a few %), but larger

inaccuracies exist beyond this range. A more accurate approximation comes directly from

the classical solution to Maxwell’s equations for damped Lorentz oscillators, resulting in the

Sellmeier equation:

FIGURE 3.5  Different fluorescence illumination modes. (a) Wide-​field epifluorescence using laser excitation. (b) Oblique

epifluorescence or highly inclined and laminated optical sheet illumination. (c) Total internal reflection fluorescence (TIRF)

using the objective lens method. (d) Schematic for refraction of a laser beam incident on a glass–​water interface. (e) The

E-​field polarization vectors in the TIRF evanescent field generated during (A) p-​TIRF excitation (incident polarization vector

shown by small light-​shaded arrow is in the plane of the page and the evanescent field polarization cartwheels across the

surface) and (B) s-​TIRF excitation (the incident polarization vector shown by small circle is into the plane of the page, and

the axis of this polarization vector in the evanescent field remains parallel to this incident polarization, that is, conserved,

though the polarization vector will also periodically extend both into and out of the plane of the page). (f) Confocal micro­

scope schematic arrangement. (g) Slimfield illumination.

KEY BIOLOGICAL

APPLICATIONS: BASIC

FLUORESCENCE

MICROSCOPY

General cell biology imaging;

Imaging specific subcellular

architectures in cells with

diffraction-​limited spatial reso­

lution; Probing thin fluorescently

stained tissue samples.