Solution to 2001 Problem 100

Moving the mirror a distance of \lambda_{\text{red}}/2 causes the fringe pattern to shift by a distance equal to the distance between two fringes. Therefore, if the fringe pattern shifts so that 100,000 fringes pass across the detector for green light, the mirror must have moved a distance

\begin{align*}d = \frac{\lambda_{\text{green}}}{2} \cdot 100,000\end{align*}

The same argument can be applied to the red laser, therefore
\begin{align*}d = \frac{\lambda_{\text{red}}}{2} \cdot 85,865\end{align*}
We can combine the two equations above to give:

\begin{align*}\frac{\lambda_{\text{green}}}{2} \cdot 10^5 = \frac{\lambda_{\text{red}}}{2} \cdot 85865 \Rightarrow \lambda_{\...
Therefore, answer (B) is correct.

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