- #1
chyo
- 4
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Hi all, I would like to know whether my approach of solving for the direction vector of a refracted ray is correct.
1. Problem statement
A ray of light is incident on an interface of two mediums. The incident ray has a unit direction vector v. i and r are the incident and refracted angles, and u is the refracted ray in question. The problem is a dynamic one.
2. Attempted Solution
I first set up a normal unit vector n and another unit vector m which is at right angle to the former as shown in the figure drawn.
Since all the vectors are of unit length, the projection of v on n is (cos i)n. With that I put m = [v - (cos i)n] / |v - (cos i)n| (since m is a unit vector).
So then u = (cos r)n + (sin r)m.
To solve the coefficients, i use cos i = v.n => sin i (by trigo equation using cos i) => sin r (by snell's law) => cos r (again by trigo using sin r)
if this approach is correct, then it works for different cases of refraction too i.e the incident ray could instead be coming from the fourth quadrant and refracted into the second quadrant.
However, the catch is that the normal n must always be defined in the same direction as the incident ray. This is where I stumble; how do i ascertain if my normal is always in the same direction as the incident ray in a dynamic situation? What condition should i check for?
Thanks for reading!