Solution (source code)

= Solution

A horizontal wavelength $h$ means $\kappa=2\pi/h$. For $n=1$,
$$
\frac{(2n+1)\pi}{2\kappa h}
=\frac{3\pi}{4\pi}=\frac34.
$$
Hence
$$
\boxed{m=1+\frac9{16}=\frac{25}{16}}.
$$