Answer
$420 nm$
Work Step by Step
To find the apparent wavelength of the light, use the Doppler effect for light equation $$\lambda'=\lambda_o \sqrt{\frac{1-\beta}{1+\beta}}$$ Since $v=0.42c$ and $v=\beta c$, $\beta=0.42$. Using known values of $\beta=0.42$ and $\lambda_o=650nm$ yields an apparent wavelength of $$\lambda '=(650nm)\sqrt{\frac{1-0.42}{1+0.42}}=420nm$$
