In this post we are going to understand the exponential factor in Beer – Lambert’s law, by assigning imaginary values to different parameters in the law. This little exercise will help us to understand the law better.
In post 160, we studied an exponential expression for Beer – Lambert’s law –
It = Io e – αc
Beer Lambert’s law has an exponential /logarithmic term in it which shows us that the intensity of the transmitted light (It) decreases exponentially with thickness and concentration of the medium. Now, let us try to understand this concept with an example.
Suppose we have a medium with 1 unit thickness and we shine 100 units of light on it.
Thus, the intensity of incident radiation (Io) =100.
Suppose this medium absorbs 50% of the incident light. This means that the remaining 50% of light is transmitted.
Thus, the intensity of transmitted light (It) = 50.
STEP 2 –
If we further pass this 50% transmitted light through 1 unit thickness of the same medium again, 50% of that light will be absorbed by the medium. In this case, Io = 50.
50% of this light will be absorbed.
50% of 50 = 25.
Thus, the intensity of transmitted light ( It ) = 50-25 = 25.
STEP 3 –
Continuing to pass this light with 25% intensity, through 1 unit thickness medium again, we get 50% of 25 = 12.5 % intensity of light absorbed.
Thus, the intensity of transmitted light ( It ) = 25-12.5 = 12.5 %
STEP 4 –
The intensity of light decreases exponentially again and the intensity of transmitted light becomes 50% of 12.5 = 6.25%.
As seen from the above example, the intensity of transmitted light is NOT decreasing linearly. It is an exponential decrease i.e the value decreases by a different amount each time –
|Step No||Decrease in It value|
|STEP 1||100-50= 50|
|STEP 2||50 – 25 = 25|
|STEP 3||25-12.5 = 12.5|
|STEP 4||12.5-6.25 = 6.25|
If we plot these values on a graph, we will get an exponential decrease curve as shown below –
In a linear decrease, the value of the intensity of transmission would decrease by a specific amount say 20 units each time. For example, It values would be 80, 60, 40, 20 for each step respectively. In this case we would get a linear curve like the one shown below-
Can you see the difference between the two graphs shown above? Thus, we now know that the Beer – Lambert’s law is an exponential expression and thus, it will give us an exponential curve.
In the next post we will solve some numericals based on the Beer – lambert’s law. Till then, be a perpetual student of life and keep learning…
Good day !