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The early-type star $\gamma$ Cas illuminates the reflection nebulae IC 59 andIC 63, creating two photo-dissociation regions (PDRs). Uncertainties about thedistances to the nebulae and the resulting uncertainty about the density of theradiation fields incident on their surfaces have hampered the study of thesePDRs during the past three decades. We employed far-UV -- optical nebula --star colour differences of dust-scattered light to infer the locations of thenebulae relative to the plane of the sky containing $\gamma$ Cas, finding IC 63to be positioned behind the star and IC 59 in front of the star. To obtain thelinear distances of the nebulae relative to $\gamma$ Cas, we fit far-infraredarchival $\textit{Herschel}$ flux data for IC 59 and IC 63 with modifiedblackbody (MBB) curves and relate the resulting dust temperatures with theluminosity of $\gamma$ Cas, yielding approximate distances of 4.15 pc for IC 59and 2.3 pc for IC 63. With these distances, using updated far-UV flux data inthe 6 eV - 13.6 eV range for $\gamma$ Cas with two recent determinations of theinterstellar extinction for $\gamma$ Cas, we estimate that the far-UV radiationdensity at the surface of IC 63 takes on values of $G_0$ = 58 or $G_0$ = 38with respective values for E(B-V) for $\gamma$ Cas of 0.08 and 0.04 mag. Thisis a substantial reduction from the range 150 $\le$ $G_0$ $\le$ 650 used for IC63 during the past three decades. The corresponding, even lower new values forIC 59 are $G_0$ = 18 and $G_0$ = 12.

The 3D Geometry of Reflection Nebulae IC 59 and IC 63 with their illuminating Star Gamma Cas