\[t'=\frac{t-\frac{vt}{c}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}=\frac{t-t_v}{\sqrt{1-\frac{v^{2}}{c^{2}}}}=\frac{2t_2}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\]