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MermaidWonders

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For what ratio of slit width to wavelength will the first minima of a single-slit diffraction pattern occur at $\pm 90°$?

The thing is, when I did it, I used the formula $sin\theta = \frac{n\lambda}{a}$, and used the fact that $m = 1$ and $\pm 90°$ to solve for $\frac{a}{\lambda}$. However, I don't know if we're supposed to plug in $-90°$ for $sin\theta$, because that would mean that our ratio of $\frac{n\lambda}{a}$ would be $-1$ as opposed to just $1$ (when $sin90°$ was plugged in)...

The thing is, when I did it, I used the formula $sin\theta = \frac{n\lambda}{a}$, and used the fact that $m = 1$ and $\pm 90°$ to solve for $\frac{a}{\lambda}$. However, I don't know if we're supposed to plug in $-90°$ for $sin\theta$, because that would mean that our ratio of $\frac{n\lambda}{a}$ would be $-1$ as opposed to just $1$ (when $sin90°$ was plugged in)...

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