Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-19 GTBL042-Callister-v2 September 13, 2007 13:59

Revised Pages

19.8 Transmission • 771

And, finally, solving forβ, realizing thatIT′/I 0 ′=0.98 andx=200 mm, yields

β=−

1

x

ln

(

IT′

I′ 0

)

=−

1

200 mm

ln(0.98)= 1. 01 × 10 −^4 mm−^1

Concept Check 19.5

Are the elemental semiconductors silicon and germanium transparent to visible

light? Why or why not?Hint:you may want to consult Table 12.3.

[The answer may be found at http://www.wiley.com/college/callister (Student Companion Site).]

19.8 TRANSMISSION

The phenomena of absorption, reflection, and transmission may be applied to the

passage of light through a transparent solid, as shown in Figure 19.7. For an incident

beam of intensityI 0 that impinges on the front surface of a specimen of thicknessl

and absorption coefficientβ, the transmitted intensity at the back faceITis

Intensity of radiation

transmitted through

a specimen of

thicknessl,

accounting for all

absorption and

reflection losses

IT=I 0 (1−R)^2 e−βl (19.19)

whereRis the reflectance; for this expression, it is assumed that the same medium

exists outside both front and back faces. The derivation of Equation 19.19 is left as a

homework problem.

Thus, the fraction of incident light that is transmitted through a transparent

material depends on the losses that are incurred by absorption and reflection. Again,

the sum of the reflectivityR, absorptivityA, and transmissivityT, is unity according

l

Incident beam

Transmitted beam

IT = I 0 (1 – R)^2 e – l

I 0

Reflected beam

IR = I 0 R

Figure 19.7 The transmission of light through a transparent medium for which there is

reflection at front and back faces, as well as absorption within the medium. (Adapted from

R. M. Rose, L. A. Shepard, and J. Wulff,The Structure and Properties of Materials,Vol. IV,

Electronic Properties.Copyright©c1966 by John Wiley & Sons, New York. Reprinted by

permission of John Wiley & Sons, Inc.)