t_{r} = t_{1} + t_{2}

t_{r} = t_{b}γ = t_{b} \frac{1}{\sqrt{1 − (\frac{v^{2}}{c^{2}}} )}

\begin{aligned}t_{b} & = \frac{2H}{c} \\ t_{r} & = \frac{2H}{c} \frac{1}{1 − (\frac{v^{2}}{c^{2}} )} ≠ \frac{2H}{c} \frac{1}{\sqrt{1 − (\frac{v^{2}}{c^{2}} )}} \end{aligned}

H = H \sqrt{1 − (\frac{v^{2}}{c^{2}} )} = H \frac{1}{γ}

L = v \frac{1}{2}(Δt)_{red}

R = \sqrt{H^{2} + (\frac{1}{2}vΔt_{r})^{2}}

Δt_{r} = \frac{2R}{c} = \frac{2\sqrt{H^{2} + (\frac{1}{2}vΔt_{r})^{2}}}{c}

Δt_{r} = \frac{2H}{c} \frac{1}{\sqrt{1 − (\frac{v^{2}}{c^{2}}} )}

γ ≡ \frac{1}{\sqrt{1 − (\frac{v^{2}}{c^{2}}} )}

\begin{aligned}Δt_{b} & = \frac{2H}{c} \\ Δt_{r} & = \frac{2H}{c} γ \end{aligned}