Determination of wavelength by hartmann's dispersion formula
Answers
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.