= Solution
The photon propagates along $-x$ in the tunnel frame and has <energy> $E_\gamma=hc/\lambda_0$ and <momentum> $p_x=-E_\gamma/c$. A <Lorentz transformation> into the approaching runner's frame gives
$$
E'_\gamma=\gamma(E_\gamma-vp_x)=\gamma(1+\beta)E_\gamma.
$$
Since $E'_\gamma=hc/\lambda'$, the approaching-source <relativistic Doppler effect> is
$$
\boxed{\lambda'=\frac{\lambda_0}{\gamma(1+\beta)}=\lambda_0\sqrt{\frac{1-\beta}{1+\beta}}.}
$$
It is a blueshift. With $q=\lambda'/\lambda_0=500.0/589.1$, solving $q^2=(1-\beta)/(1+\beta)$ gives
$$
\boxed{\beta=\frac{1-q^2}{1+q^2}=\frac{589.1^2-500.0^2}{589.1^2+500.0^2}\simeq0.16253,
\qquad v\simeq4.873\times10^7\,\mathrm{m\,s^{-1}}.}
$$
This shift depends on the relative <velocity> along the light ray, not on the tunnel length or the location of detection.
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