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(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)
=.9063sina -.4226cosa
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(.....)
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.
To find the angle at which the light would need to enter the glass to be deviated by a certain amount, you can use Snell's Law, which relates the angles of incidence and refraction to the refractive index of the medium.
Snell's Law states that:
sin(angle of incidence) / sin(angle of refraction) = refractive index
You have already used this equation to find the refractive index when given the angles of incidence and refraction.
Now, to determine the angle of incidence for a desired deviation of 25 degrees, you can rearrange the equation:
sin(angle of incidence) / sin(angle of refraction) = refractive index
to:
sin(angle of incidence) = sin(angle of refraction) * refractive index
Let's denote the angle of incidence as "a" and the angle of refraction as "b." Therefore, we have:
sin(a) = sin(b) * refractive index
Now, we substitute the known values:
sin(a) = sin(25) * 1.54
sin(a) = 0.4226 * 1.54
sin(a) = 0.6513
To find the angle of incidence "a," we take the inverse sine (arcsin) of 0.6513:
a = arcsin(0.6513)
Using a calculator or a computer program, you can find that the angle of incidence "a" is approximately 41.17 degrees.
Therefore, if you want the light to be deviated by 25 degrees, you need to enter the glass at an angle of approximately 41.17 degrees.
I hope this explanation helps! Let me know if you have any further questions.