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Reflection and Refraction, much index of refraction 
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#1
Jan2809, 12:06 PM

P: 28

1. The problem statement, all variables and given/known data
1. The index of refraction for water is 1.33 and that of glass is 1.50. a. What is the critical angle for a glasswater interface? b. In which medium is the light ray incident for total internal reflection? 2. Relevant equations n_{i}sin[tex]\vartheta[/tex]_{i}=n_{r}sin[tex]\vartheta[/tex]_{r} 3. The attempt at a solution a. I think the answer to a. is 62.46 degrees, but I am not sure. b. I think the answer is glass, simply because it is going to be moving from a less dense area to a more dense area. 


#2
Jan2809, 12:46 PM

P: 141

Use Snell's law:
[tex]n_1\sin\theta_1 = n_2\sin\theta_2\ .[/tex] Note: It's not additive like you suggested. At the critical angle, [tex]\theta_2[/tex] is 90 degrees (the light refracts along the boundary). That is to say, it's sin is 1. We can therefore rearrange for the critical angle: [tex]\theta_{\mathrm{crit}} = \sin^{1} \left( \frac{n_2}{n_1} \right)[/tex] Now we have two refractive indices, the glass and the water. If you plug them in incorrectly, you're going to end up with trying to find the inverse sin of a value > 1, which isn't possible as this has no solution. 


#3
Jan2809, 12:59 PM

P: 28

Anyway, I appreciate the input, but if you are using [tex]\theta_{\mathrm{crit}} = \sin^{1} \left( \frac{n_2}{n_1} \right)[/tex], would it not be possible to put 1.33 (n_{2}) over 1.5 (n_{1})? This would look like [tex]\theta_{\mathrm{crit}} = \sin^{1} \left( \frac{1.33}{1.5} \right)[/tex] and if plugged into a calculator, would return 62.45732485 degrees. 


#4
Jan2809, 01:05 PM

P: 10

Reflection and Refraction, much index of refraction
For this problem I calculated 62.4 degrees, the same thing you got.
As for B, I put water. 


#5
Jan2809, 01:08 PM

P: 141

Yes, that's correct as you've stated.
It also gives you the answer to your second question as [tex]n_2[/tex] represents the refractive index of the medium that the light travelling in medium [tex]n_1[/tex] is incident on. 


#6
Jan2809, 01:08 PM

P: 28




#7
Jan2809, 01:10 PM

P: 28




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