What is Hartmann Dispersion Formula?

 

Hartmann dispersion formula is a semi-empirical formula. It is also referred to as Cornu Hartmann formula. It relates refractive index (n) with the wavelength (λ). It is given by: 

n (λ)= X + Y/( λ-Z)............................................................Equation 1 

X, Y, and Z are empirical constants while n (λ) is the refractive index of a material of light of wavelength λ. The constants derived as follows:

Z= [(n1-n2)/ (n2-n3) λ1 (λ2- λ3) - λ3- λ3 (λ1- λ2)]/ [(n1-n2)/ (n2-n3) (λ2- λ3)-(λ1- λ2)]-....................................................................................Equation 2 

Y= (n1-n2)/ [1/ (λ1-Z)-(1/ (λ2-Z)…………………………Equation 3 

X=n1-B/ (λ1-Z)…………………………………………...Equation 4 

Hartmann dispersion formula is applied in the measurements of spectra wavelengths taken on a prism instruments. 
Constant Z is the spectrometer optical function. In the laboratory, it usually measured by lab technicians for every spectrometer and it is labeled on the side of every spectrometer.
Equation 1 can be written as: 

y (n(λ))=Y/ ( λ-Z) + X …………………………………...Equation 5

By plotting values of y against (λ-Z) gives a straight line in which the values of constants Y and X can be obtained.  

The pros of using the Hartmann dispersion equation technique (plotting) to determine constants
  • ·         It requires fewer calibration points.
  • ·         It is stress-free to draw.
  • ·         It is accurate 

The cons of using the Hartmann dispersion equation technique (plotting) to determine constants
  • ·         You must rely on the observations made by someone else.
  • ·         Reading from the plotted graph’s straight line values does not give λ directly.

                                            References
Forziati, F., A.(1950). Refractive index as a function of wavelength for sixty APS-NBS hydrocarbons. Journal of Research, 44, 373-385.

Wood, A., L., & Tilton, W., L. (1949). Refractive index of natural rubber for different wavelengths. Journal of Research, 43, 57-64.

Comments

Post a Comment

Popular posts from this blog

How to write a Forensic Case Study: Murder of Junko Furuta

Image
Photo of Junko Furuta  For one to score high marks in a Forensic Case Study, one must  adhere to the following: Background of the case: This section contains details about the crime. It includes; the reasons for committing the offense, the conditions which the crime was committed, the circumstances of the crime scene and clear identification of the suspect(s) and the victim(s). One should ensure that the information in this part gives a precise idea of what the case is all about.   Pick and Write an article on Iwriter Website Evidence: This encompasses the piece of evidence found at the crime scene. The evidence should be described in details, that is, ways in which the evidence was collected, processed and preserved.   Forensic Tests: The tests should be two or more that were used to analyze the evidence. The science or theory of instrumentation used must be described fully.   Results: This consists of a detailed explanation of the forensic tests and the data inter
Read more

Roles of Sodium Carbonate when Extracting Caffeine from Tea Leaves

Image
A student failed to add sodium carbonate (Na 2 CO 3 ) when extracting caffeine from tea leaves with hot water. Though, high yield of caffeine was produced. The crystals melted at temperatures between 202  and 214 degree  Celsius. Explain. This happened because sodium carbonate did not interfere with the caffeine content of the tea leaves. Sodium carbonate (which is a base) deprotonates the phenolic hydroxyl group (-OH) (acidic) of tannins rendering them anionic. Hence, making them highly soluble in water, but parsimoniously soluble in methylene chloride. So, if sodium carbonate is not added when extracting caffeine with hot water, the extracted caffeine would also contain tannins. Additionally, sodium carbonate is added during the extraction to keep caffeine (an alkaloid which is an organic base)  in a free base form. It prevents caffeine from reacting with available acid available, which may lead to the formation cation. It reacts with a phenolic hydroxyl group
Read more