Three equally spaced lines is the signature of the normal (Lorentz) Zeeman triplet. The frequency displacement of each outer line equals the Larmor precession frequency $\nu_L = \dfrac{eB}{4\pi m_e}$.
Work directly in wavelength. Differentiating $\nu = c/\lambda$ gives $|d\nu| = \dfrac{c}{\lambda^2}|d\lambda|$, so the measured wavelength gap of the adjacent lines corresponds to
\[\Delta\nu = \frac{c\,\Delta\lambda}{\lambda^2} = \frac{(3\times10^{8})(1.7\times10^{-12})}{(3.5\times10^{-7})^2}.\]
Evaluate the numerator $= 5.1\times10^{-4}$ and denominator $= 1.225\times10^{-13}$, giving $\Delta\nu = 4.16\times10^{9}\ \text{Hz}$.
Now invert the Larmor relation for the field: $B = \dfrac{4\pi m_e \Delta\nu}{e} = \dfrac{4\pi (9.11\times10^{-31})(4.16\times10^{9})}{1.6\times10^{-19}}$.
The numerator is $4.76\times10^{-20}$, and dividing by $1.6\times10^{-19}$ yields $B \approx 0.30\ \text{T}$, matching the direct estimate.
\[\boxed{B \approx 0.3\ \text{T}}\]