What is the Dispersive Power of Glass and How is it Calculated?

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Homework Statement

The dispersive power of glass is defined as the ratio \frac{n_{F} - n_{C}}{n_{D} - 1}, where C, D, and F refer to the Fraunhofer wavelengths, λ_{C} = 6563 \stackrel{o}{A}, λ_{D} = 5890 \stackrel{o}{A}, and λ_{F} = 4861 \stackrel{o}{A}. Find the approximate group velocity in glasss whose dispersive power is frac{1}{30} and for which n_{D} = 1.50.

Homework Equations

The Attempt at a Solution

I start off with the given information
\frac{n_{F} - n_{C}}{n_{D} - 1} = \frac{n_{F} - n_{C}}{1.50 - 1} = \frac{1}{30} = \frac{n_{F} - n_{C}}{.5}
I simplify
n_{F} - n_{C} = \frac{1}{60} = Δn
I know that
Δλ = λ_{F} - λ_{C} = 4861 \stackrel{o}{A} - 6563 \stackrel{o}{A} = -1702 \stackrel{o}{A}
I use the formula for group velocity
v_{g} = v_{p}(1 + \frac{λ}{n}\frac{dn(λ)}{dλ})
I use the approximation that
\frac{dn(λ)}{dλ}) ≈ \frac{Δn}{Δλ} = \frac{1}{60(-1702 \stackrel{o}{A})}
v_{g} = v_{p}(1 - \frac{5890 \stackrel{o}{A}}{1.5}\frac{1}{60(1702 \stackrel{o}{A})})
simplify and round to three decimal places
v_{g} = v_{p}(1 - 3.845x10^{-2})

From here I'm not really sure what to do. Someone told me that I should use v_{p} = \frac{c}{n}. However I'm not sure how this is correct as v_{p} = \frac{ω_{p}}{k_{p}}.

Thanks for any help.

 

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never mind