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Snell's law, critical angle & refraction 
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#1
May1310, 03:04 PM

P: 14

1. The problem statement, all variables and given/known data
Given a three layer model  [tex]v_1=1.5[/tex]km/s  [tex]v_2=1.3[/tex]km/s  [tex]v_3=2.0[/tex]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 [tex]\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}[/tex] 3. The attempt at a solution To find the critical angle, you normally take [tex]\sin \theta_c = \frac{v_1}{v_2}=\frac{1.5}{1.3}[/tex]. But in this case that means I have to take [tex]\sin^{1}[/tex] of a value that is over 1! How do I solve this? 


#2
May1410, 07:46 AM

HW Helper
P: 4,439

According to Snell's law
n1sin(θ1) = n2sin(θ2) If θ1 is θc, then θ2 = 90 degrees. So sin(θc) = n2/n1 


#3
May1410, 10:21 AM

P: 14

[tex] \frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}=\frac{n_2}{n_1} [/tex] Why does the subscript change in the [tex]n_n[/tex] ? Isnt [tex]v_1=n_1[/tex] and [tex]v_2=n_2[/tex]? Thanks for answering 


#4
May1510, 12:17 AM

HW Helper
P: 4,439

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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