# Snell's law, critical angle & refraction

by sveioen
Tags: angle, critical, refraction, snell
 P: 14 1. The problem statement, all variables and given/known data Given a three layer model ------------------------------------------------- $$v_1=1.5$$km/s ------------------------------------------------- $$v_2=1.3$$km/s ------------------------------------------------- $$v_3=2.0$$km/s Assume a ray goes through layer 1 and hits the interface between layer 1 and layer 2. What is the critical angle? 2. Relevant equations Snells law $$\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}$$ 3. The attempt at a solution To find the critical angle, you normally take $$\sin \theta_c = \frac{v_1}{v_2}=\frac{1.5}{1.3}$$. But in this case that means I have to take $$\sin^{-1}$$ of a value that is over 1! How do I solve this?
 HW Helper P: 4,442 According to Snell's law n1sin(θ1) = n2sin(θ2) If θ1 is θc, then θ2 = 90 degrees. So sin(θc) = n2/n1
P: 14
 Quote by rl.bhat According to Snell's law n1sin(θ1) = n2sin(θ2) If θ1 is θc, then θ2 = 90 degrees. So sin(θc) = n2/n1
When I look up Snell's law on Wikipedia it says

$$\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}=\frac{n_2}{n_1}$$

Why does the subscript change in the $$n_n$$ ? Isnt $$v_1=n_1$$ and $$v_2=n_2$$?

HW Helper
P: 4,442

## Snell's law, critical angle & refraction

According to the definition,
refractive index n = c/v. where c is the velocity of light in vacuum and v is the velocity in the refracting medium.
So v = c/n
Or v1 = c/n1 and v2 = c/n2
then v1/v2 = .....?

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