Answer
$L=273nm$
Work Step by Step
We know that
$2L=(m+\frac{1}{2})(\frac{\lambda}{n_2})$
This can be rearranged as:
$L=(m+\frac{1}{2})(\frac{\lambda}{2n_2})$
We plug in the known values to obtain:
$L=(1+\frac{1}{2})(\frac{382}{2\times 1.75})=273nm$
