In going over problem 1 on homework 5, I asserted (via Wolfram Alpha) that solving the equation
$ n\lambda = d^\prime - d = \sqrt{\left(x+h\right)^2 + R^2} - \sqrt{\left(x-h\right)^2 + R^2}$
for x resulted in
$x = n\lambda\sqrt{\frac{4R^2+4h^2-\lambda^2n^2}{16h^2-4\lambda^2n^2}} \label{eq:alpha}$
If you can prove this with pencil and paper, showing all your steps, I'll give you 50% bonus credit on question 1 of homework 5. Include your work and a note indicating that you'd like to be considered for the bonus credit.
$ n\lambda = d^\prime - d = \sqrt{\left(x+h\right)^2 + R^2} - \sqrt{\left(x-h\right)^2 + R^2}$
for x resulted in
$x = n\lambda\sqrt{\frac{4R^2+4h^2-\lambda^2n^2}{16h^2-4\lambda^2n^2}} \label{eq:alpha}$
If you can prove this with pencil and paper, showing all your steps, I'll give you 50% bonus credit on question 1 of homework 5. Include your work and a note indicating that you'd like to be considered for the bonus credit.
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