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 operate as described by the single straight line relationship between intensity and brightness illustrated in the graph. Rather, the eye adapts over time to increases and decreases in light intensity. At each level of adaptation a function can describe the relationship between the light intensity physical variable and the brightness psychological variable.

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 a separate 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 awareness of brightness differences occur only for intensity differences in the range of intensities in which the curve shows positive slope.

A key feature of the function describing the relationship between intensity and brightness is that the full range of brightness is available only within a narrow range of intensities at one particular time and at the adaptation level of the eye for that time. For normal operation of the eyes, this relationship between intensity and brightness is wonderful in that small intensity differences are amplified to become much larger brightness differences than would occur without amplification.

A drawback in the relationship is that no brightness differences exist for large portions of the intensity variable. The receptors of the eye can adapt and thereby respond to a broader range of intensities, preserving the amplification. The eyes adapt very slowly when light intensity is decreased because a chemical change in receptors is needed. Adaptation to light increases is nearly instantaneous as there is no underlying chemical change that needs to occur.

Consider the black appearing curve as the function for an eye adaptation level. A rapid increase in light intensity will shift the curve to the right. The difference between the Statue and background illumination will fall in the flat portion of the curve and no brightness difference occurs in the red appearing curve instance.

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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