What kind of "spectrum" do you have? Absorption spectrum? Transmission spectrum? Reflection spectrum?
From the absorption spectrum, you will need to use the Kramers-Kroenig relation. From transmission and reflection you will need to follow standard procedures from ellipsometry.
It is difficult to obtain exact relation between UV-Visible absorption and refractive index of material. In order to find the absorption coefficient Beer-Lambert Law is used.
http://pubs.acs.org/doi/pdf/10.1021/ma00036a008 will help you to connect the refractive index and absorbance of material.
In order to estimate corresponding refractive index with wavelength Cauchy’s equation will be useful. https://www.quora.com/Whats-the-Relation-between-refractive-index-of-the-medium-and-wave-length-of-the-incident-light-ray
Refractive index =speed of light/Velocity of light in medium. U know the light velocity in the. Chosen medium u can easily calculate
You can also use envelope method to find the refractive index from reflection or transmission spectra.
Article Determination of dynamic variations in optical properties of...
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