Hover over the menu bar to pick a physics animation.

## Animation of Convex Lens Refraction

Please see Focal Length Calculation
for a description of the graphics and for a first order (Snell's law) calculation of the
lens focal length, `f`.

Also note that, at startup and after moving a slider, calculation of the focal intensity takes some time.
Rather than showing the refracted RAYS that follow Snell's law of refraction, here we show incident and refracted WAVES
The reason for this is that any of the oscillating charges in the lens can and DO emit in a wide variety of angles
but only the emissions at the angles given by Snell's law result in coherent addition of the field phases at the lens axis.
In the case of a convex lens, the axial position where the coherent addition takes place is a distance of R/(n-1)
from the apex of the lens and that is what is shown here where `R` is the radius of curvature of the lens surface.
This animation shows microscopic details of the incident wave, dipole motion, and the exiting wave.

The waves are depicted by sinusoid variation of electric fields and the dipoles inside the lens
move in synchronism with the moving wave.
Note that the surface positive charge displacements (red) move inward toward the apex of the lens curved
surface as the wave proceeds. That is just the movement of the tangential component of the incident wave vector
which follows from Snell's law which states that the tangential component of the incident wave vector is continuous
at the interface.

Also note that, when very large Phase Step Rate (high frequency or short wavelength) is chosen,
the refracted waves near where they cross the lens axis are incoherent except near the focal length of the lens, f=R/(n-1)
where n is the index of refraction and R is the radius of curvature.
At each new slider setting and at startup, I've also plotted in black the Focal Intensity versus wave
crossing positions on the axis of the lens.

The black vertical line is at distance `f=R/(n-1)` from the center of the lens and the peak of the focal intensity is
generally very close to but a little short of this this line. Here `n` is the index of refraction of the lens.

In order to make the Focal Intensity distribution
very narrow we must have very short wavelengths as well as a large number of waves.