Snell’s Law

Snell’s Law is defined as:

n_isinӨ_i = n_RsinӨ_R

…where n_i is the index of refraction in the initial medium, Ө_i  is the angle of incidence, n_R is the index of refraction in the refracted medium, and Ө_R is the angle of refraction. We can use this formula to find any of the factors in that equation (e.g., what the angle of refraction is or what the index of refraction is for a medium).

Sample Problem:

Light is travelling through air at an angle of 32 degrees and passes into an unknown substance, such that it refracts at an angle of 12.5 degrees. What is the index of refraction of that substance?

To Solve:

List of what we know:                                                                                                                  ni: 1.00029 (air is always about 1)                                                                                        Ө_i : 32 degrees                                                                                                                                n_R : ?                                                                                                                                                   Ө_R : 12.5 degrees

So we use our equation…
n_isinӨ_i = n_RsinӨ_R
Then we isolate the variable we’re solving for…
n_isinӨ_i = n_RsinӨ_R
——–        ——–
sinӨ_R             sinӨ_R 

n_R = n_isinӨ_i
          ———
             sinӨ_R

Now we can plug in the values…
n_R = (1.00029sin32)
              ————–
                  sin12.5
n_R = 2.44 (approx.)

If we then refer to a table with given indexes of refraction, we can also determine that the substance is diamond.