## Rottnest Island Biophysics Field Trip 1997

### 1st and 2nd April 1997, Wadgemup Hill UWA Research Station.

Staff: Tracey Fisher, Cyril Edwards,
Rosalind Sadleir, Roger Price,

Jon Dobson, Ralph James,

Tim StPierre, Jonathon Thwaites,

Liesl Folks, Len Zuks

Rottnest is a Perth 'secret' - an island within sight of the stretching metropolitan beaches, lurking just this side of the horizon with its promise of carefree, carfree recreation. It was not always so. Joined to the mainland during the time of the Pharaohs, it became known as Wadjemup to the local Aborigines, only to be transformed by European exploitation. Bill Vlamingh stopped there in 1696 - 300 years ago last December. Named by the sailors for its resident quokka population, it passed through early efforts at farming - mainly pasture - followed by a period of ignominy as a prison for dissident Perth natives. By the end of last century it had reverted to a sleepy hunting preserve for the local vice-regals and gentry.
In 1896 Charles Yelverton O'Connor, a man of immense reknown and legend, while building water pipelines to Kalgoorlie for the gold boomers, constructing dams and reshaping ports and harbours, also managed to find time to construct Australia's first ever rotating beam lighthouse - a wonderful sturdy icon perched atop Wadjemup Hill 47m above the surrounding Indian Ocean. The single immovable beacon has its light focussed by a rotating octagonal Fresnel lens system floating on a pool of mercury, producing eight strong beams that each encircle the hill once a minute. The resulting display presents a baffling confrontation with perspective and the nature of human vision. From my experience trying to describe it to friends and colleagues who have since visited it, words are inadequate at conveying a clear picture - let us merely say that you must really experience it to grasp the peculiarity of the various situations.

One way to resolve what we see at various viewpoints looking in various directions is to imagine the infinite horizontal flat plane centred on the lighthouse that contains the light beams as they sweep the horizon. Viewing the beams in this plane is simple and clear - uniform circular rotation that may be represented mathematically by

*alpha = 2 * Pi * frequency * time*

where *alpha* refers to the angle of the beam relative to some chosen direction and *frequency* is the constant rotation rate in cycles per second. Consider now someone viewing a lighthouse of height h (relative to the observer) from a position at a distance r from its base. At a moment in time when the beam in question is behind the observer, it appears as a straight line that meets the horizon at an angle *beta* with respect to vertical. If we imagine the line of sight from the observer's eye to this point on the horizon we have the case of two parallel lines (the light beam and the line of sight) that appear to meet at infinity. We can solve the geometrical situation by looking at two triangles involving the lighthouse, the observer and the infinity point, yielding the result:

*tan(beta) =(r/h)* tan(alpha)*

The above animation was created using *Mathematica3.0* for the case of *r = 4 h*.

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