1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Dispersive power of glass

  1. Nov 24, 2013 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

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

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

    Thanks for any help.
  2. jcsd
  3. Nov 24, 2013 #2
    never mind
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted