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Homework Help: Finding speed of light through medium, when given critical angle of refraction

  1. Jan 21, 2009 #1
    1. The problem statement, all variables and given/known data
    The critical angle of refraction for calcite is 68.4 (degrees) when it forms a boundary with water. Use this information to determine the speed of light in calcite.

    2. Relevant equations
    n= Index of refraction
    c= Speed of light in a vaccum
    v= Speed of light in medium

    3. The attempt at a solution

    I am looking for v so i rearranged the equation to look like this: v=c/n

    v= (3x10^8)/68.4= 4385964.91228

    Is this right? Did the water have something to do with the equation? If not then could you please help, I have no idea how to work this problem otherwise.
  2. jcsd
  3. Jan 21, 2009 #2
    First, and perhaps most significantly, 68.4 degrees is an angle... not an index of refraction (which you have plugged it in as). You also should look up what "critical angle" means... since you will need to use this angle as one of the quantities in your calculation... a calculation that will probably first yield index (which you can then use in the equation you've shown). Hint: also look up information about "Snell's Law"... this is a refraction problem after all, and critical angle has to do with a critical point in the math of Snell's law.
  4. Jan 22, 2009 #3
    So here's what i did:

    using: sin(critical angle)= index of refraction for second medium/ Index of refraction for first medium...

    sin(68.4)= 1.333/x
    x=1.33/sin(68.4)= 1.44

    then using the the n=c/v equation:

    1.44= 3x10^8/x
    x=3x10^8/1.44= 208333333.33

    so would the answer be 2.08x10^8? also, i didn't find any use for snell's law. it would have given me the angle of incedence, which i believe is irrelevant, but i may be wrong.
  5. Feb 16, 2011 #4
    using the previous eq. u must find refractive index which is sin(angle of incidence)/sin(angle of refraction) then use the refractive index to find the speed of light in another medium by doing this:
    where c=3x10^8
    and n is the refractive index you found earlier.
    Hope this helps
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