Answer
The shortest wavelength is $425nm$
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 $m=3$
$\lambda=\frac{1700nm}{3}=567nm$
for $m=4$
$\lambda=\frac{1700nm}{4}=425nm$
Hence the shortest wavelength is $425nm$.
