Posted by Reiny on Thursday, April 19, 2007 at 6:08pm.
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
so for an angle of refection of 25º
so angle of incidence = arcsin(.658..)
That's just the application of Snell's, that part I've done. What I need is:
sin(a)/sin(a-25) = 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(x-25)
use sin(A-B)=sinAcosB - cosAsinB
sin(a-25)=sina(cos25) - cosa(sin25)
so in sina/sin(a-25)=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(.....)
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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