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unscientific
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Homework Statement
I have solved the first two parts, I'm having trouble with the final part.
Given the following relations, show the following relation of brewster angle:
[tex] tan θ = \frac {n_2}{n_1} [/tex]
Homework Equations
The Attempt at a Solution
Using:
[tex] \frac {n_2}{n1} = \frac {sin θ_1}{sin θ_3} [/tex]
Starting from:
[tex] sin 2θ_3 = sin 2θ_1 [/tex]
[tex] sin θ_3 cos θ_3 = sin θ_1 cos θ_1 [/tex]
[tex] \frac {sin θ_1}{sin θ_3} = \frac {cos θ_3}{cos θ_1} [/tex]
[tex] \frac {n_2}{n_1} = \frac {\sqrt {1 - sin^{2}θ_3}}{cos θ_1} [/tex]
[tex] \frac {n_2}{n_1} = \sqrt { \frac {1}{sin^{2}θ_1} - ( \frac {n_1}{n_2} )^{2} } tan θ_1 [/tex]
How do i show the square root term at the bottom = 1?
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