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Prove refractive index of prism (help please )

  1. Jan 9, 2008 #1
    Refractive Index Problem invloving prism (Please Help)

    1. The problem statement, all variables and given/known data
    What is given is a prism, angle of deviation and apex angle, I also have to find refractive index of the prism.

    To solve the problem I must prove that:
    Nprism = sin((A+d)/2)/ sin(A/2)


    The diagram given of the Prism:
    [​IMG]


    2. Relevant equations
    n sin(i) = nprism sin (r)


    3. My attempt at a solution

    nprism = sin(i1)/sin(r1)


    therefore i1 = (A+d)/2 and r1 = (A/2)


    just need to figure i1 = (A+d)/2 and r1 = (A/2) by proving


    Please Note: My solution so far may be completely wrong, any help given would be very much appreciated :)
     
    Last edited: Jan 10, 2008
  2. jcsd
  3. Jan 10, 2008 #2
    Does anyone have any Ideas on how to solve this, maybe a more advanced physics member on this forum may be able to shed some light on this question?
     
  4. Jan 10, 2008 #3

    malawi_glenn

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    Science Advisor
    Homework Helper

    where is d in your figure?
     
  5. Jan 13, 2008 #4
    Sorry here is the new triangle with d, please if anyone knows how to solve this question it would be very much appreciated :)

    [​IMG]
     
  6. Sep 17, 2011 #5
    Re: prove refractive index of prism (help please urgent)

    in minimum deviation position:
    i1=r2
    r1=i2 say =r
    thus, A=2r implies r=A/2
    and from equation
    d+A=i1+r2 (similarity of triangles and geometry)
    i1+r2=A+d
    thus, i=(A+d)/2

    refractive index n=[sin(A/2 + d/2)] / [sin(A/2)]
    since, n=[sin i1] / [sin r]


    hope it helped
     
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