Newsgroups: comp.graphics
From: mcdonald@aries.scs.uiuc.edu (J. D. McDonald)
Subject: Re: Raytracing transparent objects.
Date: Mon, 22 Feb 1993 16:40:25 GMT
Organization: UIUC SCS
--------------------------------------

[Another poster asks:]

     The problem:

      \
       \
        \     /  <-reflection
         \   /
          \ /
     --------------------
            \
             \
              \  <-refraction

     How much of the incoming ray is reflected, and how much is
     refracted, according to the angle, the intersecting ray hits the
     transparent object? I heard for raytracing this is only a
     constant. (Let's say, 20% are reflected, the rest goes through the
     transparent object.) But whats the solution to this problem in the
     real world? Any physicians out there? I assume (and every
     physics-book says the same), that the portions of the
     reflected/refracted ray depend on the angle (the smaller the
     angle, the smaller is the refracted portion, and vice versa), but
     in *what* way? Linear to the angle? Sinus? Arcussinus?
     Arcuscosecans hyperbolicus? :)

     Wolfram

For light polarized in the plane of incidence the fraction R reflected is

        2
     sin (I - I')
R = ----2------------
     sin (I + I')

and for that perpendicular to the plane of incidence,

        2
     tan (I - I')
R = ----2----------
     tan (I + I')

where I is angle of incidence and I' angle of refraction.

Of course sin(I') = N sin(I) / N'

For glass N' = 1.523 versus air, here's a table:

                      I (deg) R(%) parallelR(%) perp.
                        0          4            4
                        10         4            4
                        20         4            4
                        30         7            3
                        40         9            2
                        50         12          0.5
                        60         20          0.5
                        70         33           7
                        80         60          25
                        90        100          100

Ref: Smith, Modern Optical Engineering, McGraw-Hill , pp 167-168 For getting
the appearance of a complicated scene right, you can't neglect polarization.
You could do so only if all the angles of incidence are 40 degrees or less,
or if there were no sequential reflection.

Doug McDonald