Time for journey with-and-against the wind

\frac{D}{v + u} + \frac{D}{v − u} = \frac{D(v − u)}{(v + u)(v − u)} + \frac{D(v + u)}{(v + u)(v − u)}

= \frac{D(v − u)}{v^{2} − u^{2}} + \frac{D(v + u)}{v^{2} − u^{2}}

= \frac{Dv − Du}{v^{2} − u^{2}} + \frac{Dv + Du}{v^{2} − u^{2}}

= \frac{2Dv}{v^{2} − u^{2}}

Time for journey across the wind

\frac{D}{\sqrt{v^{2} − u^{2}}} + \frac{D}{\sqrt{v^{2} − u^{2}}} = \frac{2D}{\sqrt{v^{2} − u^{2}}}

if ϵ ≪ 1, (1 + ϵ)^{p} ≃ 1 + pϵ

Time for journey across the wind (again)

\frac{2D}{\sqrt{v^{2} − u^{2}}} = \frac{2D}{\sqrt{v^{2}(1 − u^{2}/v^{2})}}

= \frac{2D}{v\sqrt{(1 − u^{2}/v^{2})}}

= \frac{2D}{v} (1 − u^{2}/v^{2})^{−1/2}

Time for journey with-and-against the wind (again)

\begin{aligned}\frac{2Dv}{v^{2} − u^{2}} & = \frac{2Dv}{v^{2}(1 − u^{2}/v^{2})} \\ & = \frac{2D}{v} (1 − u^{2}/v^{2})^{−1} \end{aligned}

Δt ≃ 3.7 × 10^{−16} seconds

Δt ≃ 7.3 × 10^{−16} seconds

wavelength λ ≃ 550 nm
frequency f ≃ 5.45 × 10^{14} Hz