Characterization techniques - Micromixers Fundamentals Design and Fabrication - page 295

10 8 m/s, the corre-
sponding frequency of visible spectrum is 450-750 terahertz (10 12 Hz). The propagation velocity of an
electromagnetic wave is determined by the permeability

For the visible spectrum in Tabl e 8 .1 and the speed of light in space of c 0 ¼ 3

m em and the permittivity 3 em of the material:

1
m em 3 em

c ¼ : (8.2)

p

The refractive index of a material is the ratio between the speed of light in space and that in the
material:

c 0
c :

n ¼ (8.3)

Because the speed of light in space is the fastest, the refractive index of materials should be more than
unity. From (8.3) and (8.2) , it is apparent that for the same material, the refractive index is inversely
proportional to the wavelength. The refractive index determines the angle through which a planar
wavefront incident on an interface between two materials will be refracted from its original direction.
For instance, a light ray incident on an interface at an angle

a 1 will split into a reflected ray and
a transmitted ray, whose direction to the normal at the interface is a 2 ( Fig. 8.1 (a)):
n 1 sin a 1 ¼ n 2 sin a 2 :

(8.4)
The above effect of refraction is fundamental for making lenses, which are the basic components of an
optical microscopy system. If light passes from a medium of higher refractive index n 2 to a medium of
lower refractive index n 1 , the angle of refraction is larger than the angle of incidence. At a critical angle
of incidence

a c , the angle of refraction becomes 90 and the light is totally internally reflected
( Figure. 8.1 (b)). The effect of internal reflection can be used for making mirrors and optical fibers for
guiding lights. The critical angle can be derived from (8.4) as
a c ¼ ð n 1 = n 2 Þ:

arcsin (8.5)

FIGURE 8.1
Optical effect at an interface: (a) refraction and reflection and (b) total internal reflection.