Abstract
In this paper, an extended Young equation especially suited for an ideal cylindrical double-liquid variable-focus lens is derived by means of an energy minimization method. Based on the extended Young equation, a kind of focal length hysteresis effect is introduced into the double-liquid variable-focus lens. Such an effect can be explained theoretically by adding a force of friction to the tri-phase contact line. Theoretical analysis shows that the focal length at a particular voltage can be different depending on whether the applied voltage is increasing or decreasing, that is, there is a focal length hysteresis effect. Moreover, the focal length at a particular voltage must be larger when the voltage is rising than when it is dropping. These conclusions are also verified by experiments.
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