250 13.Optical Properties of Materials X ←-Vacuum Material ep(e】 FIGURE 13.2.Exponential decrease of the amplitude of electromagnetic radiation in optically dense materials such as metals. We define a characteristic penetration depth,W,as that dis- tance at which the intensity of the light wave,which travels through a material,has decreased to 1/e or 37%of its original value,i.e.,when: L=1=e1 (13.14) Io e This definition yields,in conjunction with Eq.(13.13), &=w=k (13.15) Table 13.2 presents experimental values for k and W for some materials obtained by using sodium vapor light (A=589.3 nm). The inverse of W is sometimes called the (exponential)atten- uation or the absorbance,a,which is,by making use of Eq. (13.15)and(13.12), a=Amk=Amk =2me2 (13.16) A c An It is measured,for example,in cm-1.The energy loss per unit length(given,for example,in decibels,dB,per centimeter)is ob- tained by multiplying the absorbance,a,with 4.34,see Problem 13.7.(1dB=101ogI1o). TABLE 13.2.Characteristic penetration depth,W,and damping con- stant,k,for some materials (A=589.3 nm) Material Water Flint glass Graphite Gold W(cm) 32 29 6×10-6 1.5×10-6 k 1.4×10-7 1.5×10-7 0.8 3.2We define a characteristic penetration depth, W, as that dis￾tance at which the intensity of the light wave, which travels through a material, has decreased to 1/e or 37% of its original value, i.e., when: I I 0
1 e
e1. (13.14) This definition yields, in conjunction with Eq. (13.13), z
W
4 c k
4  k . (13.15) Table 13.2 presents experimental values for k and W for some materials obtained by using sodium vapor light (
589.3 nm). The inverse of W is sometimes called the (exponential) atten￾uation or the absorbance, , which is, by making use of Eq. (13.15) and (13.12), 
4  k
4 c k
2   n 2 . (13.16) It is measured, for example, in cm1. The energy loss per unit length (given, for example, in decibels, dB, per centimeter) is ob￾tained by multiplying the absorbance, , with 4.34, see Problem 13.7. (1 dB
10 log I/I0). FIGURE 13.2. Exponential decrease of the amplitude of electromagnetic radiation in optically dense materials such as metals. 250 13 • Optical Properties of Materials x Vacuum Material exp – &kz c z TABLE 13.2. Characteristic penetration depth, W, and damping con￾stant, k, for some materials (
589.3 nm) Material Water Flint glass Graphite Gold W (cm) 32 29 6 106 1.5 106 k 1.4 107 1.5 107 0.8 3.2