 Wavelength linewidth of a damped-oscillator power resonance

Converting the two half-power frequencies using $\lambda =2\pi c/\omega$ gives $\Delta \lambda =2\pi c(1/{\omega }_{-}-1/{\omega }_{+})$. Since ${\omega }_{-}{\omega }_{+}={\omega }_0^2$, this reduces exactly to the displayed expression. The wavelength endpoints are not symmetric around $2\pi c/{\omega }_0$; a symmetric narrow-line sketch is an approximation. This conversion concerns the same measured response versus a reparametrized axis, not a transformation between spectral density conventions.