NWeid1
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Homework Statement
Suppose that light travels from point A to point B as shown in the figure/ Assume that the velocity of light above the boundary line is v1 and the velocity above the boundary line is v2. Find the total time T(x) to get from point A to point B, Write out the equation T'(x) = 0, replace the square roots using the sines of the angles in the figure and derive Snell's Law \frac{sinθ_1}{sinθ_2} = \frac{v_1}{v_2}
Homework Equations
The Attempt at a Solution
Here is the work I've done so far.
T(x) = \frac{\sqrt{1+x^2}}{v_1} + (-\frac{\sqrt{1+(2-x)^2}}{v_2})
T'(x) = \frac{1}{v_1\sqrt{(1+x^2)}} - \frac{1(x-2)}{v_2(\sqrt{(1+(2-x)^2)}} = 0
T'(x) = \frac{1}{v_1\sqrt{(1+x)^2}} = \frac{x-2}{v_2\sqrt{1+(2-x)^2}}
And I know I have to get
\frac{sinθ_1}{sinθ_2} = \frac{v_1}{v_2}
and I replaced the fractions with sines but the (x-2) on the right side of the equation messes up the formula, so now I'm confused.
Also! Is my latex working for you guys? What did I do wrong? lol
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