In the previous post we introduced the term absorbance. The term absorbance quantifies the amount of light absorbed by a solution. We know ,from the previous post –

We stated that absorbance and transmittance are two sides of a coin. How are they related?

Absorbance is commonly expressed in terms of Io and It , as follows –

A = log 10 (Io /It)

The following table gives the values for both A and T –

In mathematics , logarithm means opposite of an exponential.

In simple terms, log b x = y means by = x
Thus, log 10 x = y means 10 y = x
e.g. – log 10 1000 = 3 means 10 3 = 100

Also , – log (x) = log (1/x)

It’s not important, but just for you information , we can derive this expression as follows –

Graphically the relationship between A and T can be shown as –

Image Source: Stephen Gallik , Ph. D.

How to understand this graph ?

The blue line indicates that as the absorbance(A) decreases , the %T value increases. This is because both those terms are inversely proportional. However, this inverse relationship is NOT linear but a logarithmic one –
e.g – If 50% of the photons of monochromatic light are transmitted by a sample, and 50% of the photons are absorbed, T = 0.5, but A is not 0.5, A is 0.3 (inverse logarithmic relationship between T and A). 

The above graph also corroborates the relationship –

A = log 10 (1/T)

The difference between the graphs of expressions y= log 10 (x) and y= log 10 (1/x) is shown below –

Transmittance and absorbance have no units .The term optical density is an older term for absorbance and is no more used by the scientific world.

After studying the terms absorbance and transmittance and the Beer – Lamberts’s law , we shall proceed to discuss the next law of photochemistry in the next post.Till then,

Be a perpetual student of life and keep learning….

Good day !

References and further reading –

1.Physical Chemistry by W J Moore, first edition


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