Disappearing Statue of Liberty

Psychophysicists refer to light intensity as a physical variable and brightness as a psychological variable. A relationship exists between intensity and brightness. Many people believe that the relationship can be described by higher intensities yielding greater brightness. The following graph provides one depiction of the higher intensities yielding greater brightness relationship.

The human visual system does not function as described by the graph above. Rather, the eye adapts over time to increases and decreases in light intensity. The adaptive responses are called light adaptation and dark adaptation. Light adaptation occurs more quickly than dark adaptation and for instances of small, rapid intensity increases, the adaptative shift in sensitivity can occur in a fraction of a second. Dark adaptation is a slower response and total dark adaptation will take more than twenty minutes to complete, as depicted in the following graph.

The human eye operates over a broad range of intensities, from a minimum measured in photons to a maximum that is a billion times greater. Adaptive shifts in sensitivity allow the eye to function across the broad range. Each of the adaptive states can be described by an operating curve for the relationship between intensity and brightness. The operating curves in the graph below depict the brightness and intensity relationships for 5 adaptive states that could occur at different times as produced by adaptation to 5 different ambient intensities. At any one time, only one curve describes the brightness and intensity relationship. In each operating curve brightness differences occur only for intensity differences in the range of intensities in which the curve shows positive slope.

To make the an object like the Statue of Liberty disappear, the ambient light can be manipulated such that the Statue and its background are on the lower portion of the operating curve. See the graph below for a depiction of the Statue and background on an operating curve. The letter "A" shows the brightness difference that results. Sudden introduction of an ambient light intensity increase will cause a rapid adaptive shift of the operating curve with the new position indicated by the red appearing curve. The letter "B" indicates the 0 brightness difference that corresponds to the Statue and background falling on the flat, no slope portion of the shifted operating curve. In other words, no brightness difference results and people will not see a Statue against a background.

  • There are other means to accomplish the illusion of large objects disappearing. Can you identify some of the other means?
  • If you are a magician, how can you use motorcylcle headlights, panning flood and spot lights, house lights, and helicopter lights?
  • Why will the helicopter appear to fly where the Statue was located before it disappeared?
  • Why wouldn't you use dark adaptation rather than light adaptation?
  • How does the disappearance of the Statue differ from what happens every evening and night?
  • Can you see implications of the illustration that should lead car drivers to use caution at night and adopt strategies for avoiding directly looking at the headlights of oncoming cars?

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