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How to prove this equation mathematically (light / optics)

  1. Jul 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove mathematically that, for a material m in air, the since of the critical angle is given by the expression sinθc = 1/nm

    2. Relevant equations
    n = index of refraction
    m = material
    a = air
    na = 1
    critical angle = 90 degrees

    nm x sinθc = na x sinθa

    or

    Sinθa/Sinθc = nm

    3. The attempt at a solution
    I thought of plugging in the variables in the first equation and i tried rearraging it but I got this
    nm x sinθc = 1 x sinθa
    nm x sin90 = 1 x sinθa
    sinθa = nm
    and if i plugged that in to sinθa all i got was 1 = 1
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 22, 2009 #2

    rock.freak667

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    I'm not sure what you mean by m= material....

    But at θc, θa= 90 degrees. Which is the definition of the critical angle.
     
  4. Jul 22, 2009 #3

    Well θc = 90 degrees however, I thought the incident angle won't be 90 degrees celcius because i don't think both air and the unkown material have the same index of refraction
     
  5. Jul 22, 2009 #4

    rock.freak667

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    Well I assumed the light was going from the medium to the air (more optically dense to less optically dense medium).

    so the angle of refraction θa=90.
     
  6. Jul 22, 2009 #5
    No is the other way around the air into the medium I think so the angle of incident = something and angle of refraction in the medium = 90
     
  7. Jul 22, 2009 #6

    rock.freak667

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    (from a textbook paraphrased)

    [tex]n_1 sin\theta_1 = n_2 sin\theta_2[/tex]
     
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