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Math Help - frequency of light wave in liquid.

  1. #1
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    frequency of light wave in liquid.

    The frequency of a light wave is the same when the light travels in ethyl alcohol as it is when it travels in benzene. What is the ratio of the wavelength of the light in ethyl alcohol to that in benzene?

    wavelength ethyl alcohol / wavelength benzene

    also, i know that the index of refraction of Ethyl alcohol is 1.362
    and the index of refraction of Benzene is 1.501

    not sure if those calculations are relevant for the wavelengths of these liquids or not.

    This doesn't seem to be a hard ratio to calculate, but i know i'm not find the index of refraction for a material or the speed of light. Need help finding the wavelength ratio.
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    Quote Originally Posted by rcmango View Post
    The frequency of a light wave is the same when the light travels in ethyl alcohol as it is when it travels in benzene. What is the ratio of the wavelength of the light in ethyl alcohol to that in benzene?

    wavelength ethyl alcohol / wavelength benzene

    also, i know that the index of refraction of Ethyl alcohol is 1.362
    and the index of refraction of Benzene is 1.501

    not sure if those calculations are relevant for the wavelengths of these liquids or not.

    This doesn't seem to be a hard ratio to calculate, but i know i'm not find the index of refraction for a material or the speed of light. Need help finding the wavelength ratio.
    What is the speed of light in ethyl alcohol? In benzene? You can get these from the index of refraction.

    -Dan
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    Okay speed of light of ethyl alcohol is: 3.00 x 10^8 / 1.362

    and the speed of light of benzene is: 3.00 x 10^8 / 1.501

    so then i divided the speed of light of of ethyl alcohol by benzene speed of light.

    and got about 1.1

    no units then?

    thanks for the help.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by rcmango View Post
    Okay speed of light of ethyl alcohol is: 3.00 x 10^8 / 1.362

    and the speed of light of benzene is: 3.00 x 10^8 / 1.501

    so then i divided the speed of light of of ethyl alcohol by benzene speed of light.

    and got about 1.1

    no units then?

    thanks for the help.
    You have the right answer, but I'm not certain that you have the right logic chain.

    So now you have the values for the speed of light in each media. Now, from the wave speed equation we have
    v = \lambda \nu

    \lambda = \frac{v}{\nu}

    You know that the frequency of the light in both media are the same, so when you take the ratio of the wavelengths:
    \frac{\lambda _{ethyl}}{\lambda _{benzene}} = \frac{\frac{v_{ethyl}}{\nu}}{\frac{v_{benzene}}{\n  u}}

    = \frac{v_{ethyl}}{v_{benzene}}

    -Dan
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