# Calculate refractive index [closed]

Is it possible to calculate the refractive index of a material for $$wavelength = 546.07 \ nm$$, knowing that the dispersion of a prism made of this material is $$3.44 \times 10^{-5} \ nm^{-1}$$, and that the refractive index for the yellow line, $$577.96 \ nm$$ wavelength, is $$1.5171$$ ?

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• Sep 23 at 18:18
• @AslanMonahov This is not about the Fresnel equation, it is about the definition of the coefficient of dispersion. Sep 23 at 21:53
• Hint: The index of refraction is a function of the wavelength $n(\lambda)$, the (coefficient of) dispersion is given by $\frac{dn}{d\lambda}$. Now you can Taylor expand $n(\lambda)$ to the first order to approximate $n(\lambda + \Delta \lambda)$. Note that it should say, that the dispersion at a wavelength has a certain value – the dispersion is typically not constant. Sep 23 at 21:56