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posted by Reiny .
I don't know the physics behind Snell's Law, but I can do the math
Snell's Law says
sin(angle of incidence)/sin(angle of reflection) = refractive index
since you know the two angles...
sin45/sin27 = refractive index
=1.5575365
so for an angle of refection of 25º
sin(incidence angle)/sin25º=1.5575..
sin(incidence angle)=sin25(1.55..)
=.6582433
so angle of incidence = arcsin(.658..)
=41.166º
That's just the application of Snell's, that part I've done. What I need is:
sin(a)/sin(a25) = RI
I would solve it by iteration. There is no simple solution to it.
OH...you could graph it on a calculator and see where it crosses the axis. Plot y as a function of x on your graphing calculator.
y= RI  sin x /sin(x25)
use sin(AB)=sinAcosB  cosAsinB
sin(a25)=sina(cos25)  cosa(sin25)
=.9063sina .4226cosa
so in sina/sin(a25)=RI
sina = .9063(RI)sina  .4226(RI)cosa
sina  .9063(RI)sina = .4226cosa
sina(1.9063(RI)) = .4226cosa
sina/cosa = .4226/1.9063(RI))
Tana = ........
a = arctan(.....)
Hi!!
I'm a hobby gem faceter and am trying to figure out some of the math involved. What I want to know is assuming I have a piece of glass, refractive index of 1.54 (or anything for that matter) at what angle would the light need to enter it to be deviated by a certain amount?
For instance, using Snell's law, I know that if a beam of light goes into glass at a 45 degree angle (from the norm), it will travel through the glass at about 27 degrees. The light has deviated by 18 degrees. What angle would I need it to enter if I wanted it to deviate by 25 degrees?
Thanks for any help.
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