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Optical Density

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Sun light penetrates through glass window. The glass absorbs some amount of light and transmits the remaining part. At what rate it transmits light is what optical density tells. In simple words, it is the measure of ability of material to block light. Lets study more about it.

Optical Density Definition

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The optical density is defined as the measure of extent to which a object transmits the light or any electromagnetic radiation. It is indicated by refractive index $\eta$. It tells how many times that light wave would be slower in material compared to that in vacuum,
$\eta$ = $\frac{3 \times 10^8 m/sec}{V_{material\ medium}}$
where, Vmaterial medium is velocity in material medium

Optical Density Formula

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Optical Density has two formulas,
Beer's Law
According to Beer"s law it is given as
A = $\epsilon$ cl
Where, $\epsilon$ is the absorbance or optical density
c is concentration of solution
l is the path length

In spectroscopy, the optical density is termed as the absorbance of any material. It is defined as the logarithmic ratio of the radiation that falls on a material to the radiation that gets transmitted through a material.
Optical Density

Optical density formula is given by
Optical density = log10$\frac{I_o}{I_t}$
where,
$I_{o}$ represents the intensity of incident light
$I_{t}$ represents the intensity of transmitted light.

Optical density Measurement

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The optical density can be measure using instruments like photocell using light intensity. In spectroscopy it is measured using spectrophotometer for various chemistry experiments. It varies from a substance to another as given below:

Material
Refractive index
Vacuum 1.00
Air
1.0003
Ice
1.31
Water
1.333
Ethyl Alcohol
1.36
Plexi glass
1.51
Crown glass
1.52
Light Flint glass
1.58
Dense Flint glass
1.66
Zircon
1.923
Diamond
2.417
Rutile
2.907
Gallium Phosphide
3.5

Optical Density Units

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Optical density has no dimensions. Since the concentration we measure in the moles per liter and the length of path as centimeter so the commonly used unit of optical density is Liters per mole cm.

How to Calculate Optical Density?

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Lets go through some examples on optical density:

Solved Examples

Question 1: A chemical has molar absorptivity constant is 2 /Mcm. Calculate the optical density and concentration of the solution having absorbance of 0.8 and length of 1.23 cm.
Solution:
 
Given: Molar absorptivity constant $\epsilon$ = 2 /Mcm,
       Absorbance A = 0.8,
       length L = 1.23 cm
Optical density = $\frac{A}{L}$
                       = $\frac{0.8}{1.23\ cm}$
                       = 0.65 per cm.

 

Question 2: Calculate the absorption coefficient if length of path is 1.5 cm and light transmitted is 60% from a solution.
Solution:
 
Using Beer-Lambert law we have,
Absorption A = - log T = - log $\frac{I}{I_o}$
                            or
- log $\frac{I}{I_o}$ = A = $\epsilon$
   $\epsilon$ = -log (0.5)
                  = 0.0376.