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Phy 122
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critical angle
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In the middle of problem set 6 #24 we have
We can find the specific `thetaIn that satisfies this condition.
condition for critical angle: sin(`thetaIn) * n2 / n1 = 1
We easily solve this for `thetaIn:
critical angle: `thetaIn = arcsin(n2 / n1)
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I get the general idea but one step confuses me:
sin(`thetaIn) * n2 / n1 = 1
I would get the sin(`thetaIn)isolated on one side by multiplying both sides by n1/n2
This should give us
sin(`thetaIn) = n1/n2
And then `thetaIn = arcsin(n1/n2) which won't work since n1 is greater than n2. 1.54 > 1.19
???What am I missing???
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The condition was written carelessly.
The critical angle is that for which thetaOut = 90 deg.
Snell's Law says that
sin(thetaIn) / sin(thetaOut) = n2 / n1
so that for thetaOut = 90 deg, in which case sin(thetaOut) = 1, we have
sin(thetaIn) = n2 / n1
so that
sin(thetaIn) * n1 / n2 = 1.
In other words, the condition is
sin(thetaIn) = n2 / n1, not n1 / n2.
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