144 BIOPHYSICALLY ACTIVE LIGHT 



certain waveleDgths are freely transmitted while others are strongly 

 absorbed. 



Law of General Absorption 



When radiant energy passes through a homogeneous medium, the 

 medium absorbs part of the energy and the amount of this absorption is 

 generally different for various wavelengths. 



If a monochromatic beam of light has its intensity (the energy per 

 square centimeter per second of a plane parallel beam of monochromatic 

 light) decreased by an amount dl in passing through a distance dx in 

 the material, and if the loss is the same at all depths, then dl r» dx. If at 

 the same time the decrease in intensity is proportional to the intensity 

 itself (dl o* I), then 



dl = —aldx 



On integration this becomes 



I = constant e~ ax 



where a is the constant of proportionality whose magnitude depends on 

 the material and wavelength of the beam of radiant energy. The nega- 

 tive sign is used to indicate that the change in I is a decrease. 



If Jo denotes the constant intensity of the beam which enters the 

 surface of a slab of absorbing material, where x = 0, then the constant 

 in the above relation is the intensity of the incident energy, 7 . It 

 follows that the intensity of the beam after passing through a thickness 

 x = d has an intensity I d given by the relation 



Id = he~ ad 



where a is known as the coefficient of absorption. This law implies that 

 the absorption increases in geometrical progression as the thickness 

 increases in arithmetical progression. 



To illustrate the law, let us consider the slab d composed of five layers, 

 each of unit thickness, and made of a material having an absorption 

 coefficient equal to yo- Let the incident energy I = 100 units. In 

 traversing the first layer, this value is reduced y 1 ^- by absorption so 

 that 90 units leave the first and enter the next layer. The 90 units lose 

 Yq of their magnitude in the second layer, so that 81 units are incident 

 on layer three. Then layer three absorbs 8.1 units, leaving 72.9 units, 

 etc. The energy leaving the final surface of the fifth layer is only 59.0 

 units. Hence the total energy loss through absorption is 41 units. 

 The per cent transmission or transmissivity is 



T = 100 y 



