To understand how a variable focusing lens based off of electrowetting works, we should first look at some phenomena that are commonly discussed when talking about optics.  This is meant to be a brief review of lenses and key topics from geometric optics.  The goal is to take the ideas of electrowetting and combine it with optics so one can understand the fundamentals of the electrowetting variable focusing lens. 

The key topic in discussing lenses is refraction.  Refraction occurs when light travels slower in one media compared to its speed in a vaccuum.  An effect of refraction is that light can now bend instead of traveling in a straight line.  An important material property used is the index of refraction (n), which is defined as

Where c = 2.98x10⁸ m/s and v is the speed of light in the material.  The index of refraction tells us how hard is it for light to move in a material.  One way to picture the effect of traveling into a material with a higher index of refraction is to imagine that you are on a beach and start running towards the ocean.  While on the beach you can run pretty fast, but once you hit the water, the rate at which you can run reduces greatly.  The ocean represents a material with a higher index of refraction, and the beach represents the material with a lower index of refraction.  To get a feel for how light is bent when going from one material to another let's use the same analogy, however, this time you are in a long line of people running at the same speed; the line of people are running at an angle with the shoreline.  Once the first person reaches the water, their speed is slowed.  The rest of the group is still moving at a faster speed and can cover more distance.  As each person goes into the water their speed is slowed, and this continues until everyone has entered the water.  The net result is that the line has rotated a bit (see the image below).