Determine dispersion from fitting equation

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SUMMARY

The discussion focuses on determining the dispersion (dn/d lambda) at a wavelength of 800 nm using the fitting equation y = 7e-15 x + 1.60, derived from a graph of refractive index (n) versus inverse wavelength squared (1/lambda^2). The user initially attempted to differentiate the equation but overlooked the coefficient of x, leading to incorrect results. Correctly applying the derivative while considering the coefficient is essential for accurate calculations of dispersion.

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  • Understanding of calculus, specifically differentiation.
  • Familiarity with the concept of refractive index and its relation to wavelength.
  • Knowledge of fitting equations and linear regression analysis.
  • Basic understanding of optical dispersion phenomena.
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Students in physics or engineering, particularly those studying optics, as well as professionals involved in optical design and analysis.

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1. Homework Statement

Determine the dispersion (dn/d lambda) at a wavelength of 800 nm from fitting equation.


2. Homework Equations

Fitting equation from graph of n vs 1/lambda^2

y = 7e-15 x + 1.60


3. The Attempt at a Solution

Since it is a plot of n vs 1/lambda^2 I thought that x would be 1/lambda^2 so I took the derivative of that to get -2/lambda^3 and then put in the number. However I did not get a correct answer consistent with earlier findings.

What am I doing wrong?
 
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You forgot the coefficient of x.
 

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