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Homework Help: How long does it take the ray to traverse this path?

  1. Jul 11, 2009 #1
    1. The problem statement, all variables and given/known data

    A light ray enters the atmosphere of a
    planet where it descends to the surface
    15.2 km below. The index of refraction where
    the light enters the atmosphere is 1.2 and it
    increases uniformly to the surface where it has
    a value of 1.55.
    I) How long does it take the ray to traverse this path? Answer in units of s.
    II) How long would it take to cover the same distance in a vacuum? Answer in units of s.

    2. Relevant equations
    speed of light= 2.99*10^8
    delta V = C/(delta N)
    delta V= delta X / delta t

    3. The attempt at a solution

    For Question I what i did is that
    delta N = N2-N1= 1.55-1.2= 0.35
    delta V = (2.99*10^8)/(0.35) = 8.54*10^8 m/s
    delta t = 15.2*10^3/8.54*10^8= 1.779*10^-5sec

    but im not sure if my way is correct can someone please check and tell me if im going wrong somewhere

    and for II) i didnt understand what is needed therefore i didnt know how to attempt at a solution

    need your help and thanx in advance
  2. jcsd
  3. Jul 11, 2009 #2


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    Homework Helper

    V1 = C/N1
    V2 = C/N2
    delta V = C( 1/N1 - 1/N2)
  4. Jul 11, 2009 #3
    i didnt understand
  5. Jul 12, 2009 #4


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    Homework Helper

    Velocity in the medium = velocity of light in vacuum/refractive index of the medium.
    So Δv = C/N1 - C/N2
  6. Jul 13, 2009 #5
    is this a calculus-based course? because i think you would need to use calculus in a situation where the refractive index changes uniformly. as for the second part, it's much easier than you're making it. after all, the index of refraction is relative to the vacuum. for instance, in a piece of glass with index n=1.5, light travels 1.5 times more quickly in a vacuum than it does in the glass.
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