Snell's law, critical angle & refraction

[sveioen]

Homework Statement

Given a three layer model

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$$v_1=1.5$$km/s
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$$v_2=1.3$$km/s
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$$v_3=2.0$$km/s

Assume a ray goes through layer 1 and hits the interface between layer 1 and layer 2. What is the critical angle?

Homework Equations

Snells law
$$\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}$$

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?

 

[rl.bhat]

According to Snell's law
n1sin(θ1) = n2sin(θ2)

If θ1 is θc, then θ2 = 90 degrees.

So sin(θc) = n2/n1

 

[sveioen]

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 $$v_2=n_2$$?

Thanks for answering

 

[rl.bhat]

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 = ...?