The Galactic neutron star X-ray binary Her X-1 displays a well-known 35-day superorbital modulation in its X-ray and optical light curves. Detected across a broad energy range, the modulation is prevalent in X-rays, cycling between low and high states. The 35-day modulation is believed to be the result of the periodic occultation of the neutron star by a warped precessing accretion disc. Using optical observations of Her X-1 during both the anomalous low state (ALS) and the normal high state, it is shown that the orbital light curve of Her X-1 varies systematically over the 35-day precession cycle. The 35-day precessional profile is remarkably consistent between the ALS and normal high state of Her X-1, suggesting only a very slight change in the form of the disc warp between the two states. Comparison of optical and X-ray light curves suggests that a significant component of the X-ray flux during the ALS originates from the companion star.