260 BIOLOGICAL EFFECTS OF RADIATION 



I = loe-"' (2) 



or in logarithmic form 



k = ^\n -^^ (3) 



In these formulas 7o represents the incident light, I the transmitted 

 light, I the thickness of the absorbing medium and k, a constant. This 

 formula expresses Lambert's law connecting the transmission of light 

 with the thickness of the absorbing material. The absorption coefficient 

 k depends on the nature of the absorbing material but it is constant for 

 any given material. This relationship may be expressed as follows 

 in logarithms to the base 10 instead of in natural logarithms: 



^ = 7 log j" U) 



where E is defined as the extinction coefficient. 



A similar formula applies to the influence of concentration c of absorb- 

 ing material on the intensity of transmitted light. This formula is known 

 as Beer's law. 



T J -k'c I.' -2.303 , I 2.303, h ... 



1 = loe "" or k = ■ log j- = log -^ (5) 



C 1 C I 



It applies to gases and to solutions when there is no other complicating 

 change involved in the dilution process. In solution it applies only 

 when the solvent is transparent. One of the most convenient ways of 

 determining whether this law applies to a given system is to plot the 

 logarithm of the transmitted light intensity against concentration, with 

 a given thickness of material. If Beer's law is applicable, a straight line 

 results. If the line is not straight it may be suspected that chemical 

 changes such as dissociation or combination with the solvent are involved. 

 In Fig. 5 a typical plot of this kind is shown for gaseous acetone. 



Reflection of light Ir at right angles to a boundary between two differ- 

 ent media is related to the incident light /o by Fresnel's Law as given in 

 equation (6). 



The term a occurring in this formula represents the ratio of the refractive 

 indices in the two media. The refractive indices of glass, quartz, water, 

 and most liquids are sufficiently close together so that the amount 

 reflected at interfaces between these materials is negligible in most 

 photochemical investigations. When a beam of light strikes a glass-air 

 interface at right angles, it can be calculated from this formula that about 

 4 per cent of the light will be reflected backward. This reflection occurs 

 at every interface in which a gas is in contact with a solid or liquid surface. 

 Scattering of light occurs in all materials, but it is negligible in most 

 photochemical reactions unless there are a large number of surfaces such 



