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How to calculate refractive index when angle of incidence is 0?
I am doing an experiment where I point a laser beam to water and find the angle of refraction and then the index of refraction. But how can I calculate the index of refraction of water when my angle of incidence is 0? From Snell s Law that would give that the refractive index is also 0 right? but that doesn t make sense
1 Answer
- RickBLv 75 years agoFavorite Answer
> "From Snell s Law that would give that the refractive index is also 0 right?"
No, not exactly. Snell's law gives a mathematically undefined result in that case, because it involves division by zero, which is not allowed.
n₂ = (sinθ₁/sinθ₂)n₁
Whenever the angle of incidence is zero, the angle of of refraction is also zero, and sin(0)=0, so you have:
n₂ = (0/0)n₁
This expression does NOT equal zero! It is mathematically undefined.
The conclusion here is that this is a bad experiment. You cannot determine the index of refraction by using an angle of incidence of zero, because you'll always get the same result (the same (zero) angle of refraction) NO MATTER WHAT the index of refraction is. So, you need to tilt that laser!
