Answer
$660nm$
Work Step by Step
We can find the required longest wavelength as follows:
$sin\theta=\frac{m\lambda}{d}$
$\implies sin\theta=mN\lambda$ because $d=\frac{1}{N}$
This can be rearranged as:
$\lambda=\frac{sin\theta}{mN}$
We plug in the known values to obtain:
$\lambda=\frac{sin90^{\circ}}{(2)(76\times 10^{-4}m^{-1})}$
$\lambda=660\times 10^{-9}m=660nm$
