Answer
The longest wavelength is $567nm$
Work Step by Step
We know that
$2L=\frac{m\lambda}{n}$
This can be rearranged as:
$\lambda=\frac{2nL}{m}$
We plug in the known values to obtain:
$\lambda=\frac{2(1.70)(5\times 10^{-7})}{m}=\frac{1700nm}{m}$
for $m=1$;
$\lambda=\frac{1700nm}{1}=1700nm$
for $m=2$;
$\lambda=\frac{1700nm}{2}=850nm$
for $m=3$;
$\lambda=\frac{1700nm}{3}=567nm$
Hence the longest wavelength is $567nm$.
