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Problem: Decadic absorption coefficient

The decadic absorption coefficient (see Absorption coefficient), a10, of a medium in which light scattering is negligible can be defined as follows:

 a10 = - (1 / z) log10[Φ(z) / Φ(0)]  (1)

where z is the distance in a uniform medium and Φ(z) is the power of light in a collimated beam. On the other hand, the absorption coefficient for such a medium can be defined as follows:

 a = - (1 / z) ln[Φ(z) / Φ(0)]  (2)

Derive the relationship between a10 and a, given that the distance unit is the same.

CITATION:
Jonasz M. 2006. Problem: Decadic absorption coefficient (www.tpdsci.com/Tpc/AbsCfDec_P.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).
HISTORY:
Published: 05-Mar-2008
Modified: 05-Mar-2008
Peer-reviewed: PENDING
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