Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fresnel Double Prism equation

  1. Jan 23, 2005 #1

    jh

    User Avatar

    Hi,
    i need to deduce the Fresnel Double Prism equation, which states:

    d = 2a(n-1)alpha,

    according to the linked image.
    Fresnel Double Prism setup

    The distance between the constructed virtual objects S' and S'' is here called d. The distance from the light source to the prism is called a, the prism has two sides (common base) defined by the common apex angle alpha, and the refractive index n.

    Any help appreciated!!
     
  2. jcsd
  3. Jan 23, 2005 #2
    Hi jh,

    You probably know that for a single prism the deviation angle is given by
    [tex]\delta=i+i'-A[/tex]
    The refraction' law in the incidence and emergence points (for very small angles) is
    [tex]i=nr[/tex]
    [tex]nr'=i[/tex]
    and from these two equations you have now
    [tex]i+i'=n(r+r')=nA[/tex].

    It is clear now that
    [tex]\delta=nA-A=A(n-1)[/tex]

    Because you have a double prism,
    [tex]\delta_{tot}=2\delta[/tex].
    and [tex]\delta_{tot}\cdot a[/tex] for the distance between the two points (images). ( [tex]A=\alpha[/tex])
     
    Last edited: Jan 23, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fresnel Double Prism equation
  1. Fresnel Equations (Replies: 1)

Loading...