The outcome of this lesson was to explain to the students how rainbows are formed any what dictates its dimensions. During the introduciton of Snell's Law, total inernal reflection was introduced.

The change of media (air to water), causes incoming white light from the sun to split into the colors of the visible spectrum. Light is then reflected off the back of the raindrop, then further refracted as it leaves the droplet and back into the air. Due to the angles of refraction in the droplet and the critical angle from water to air (48.59 degrees), in order for a rainbow to be observed, the angle between the incoming rays from the sun and the outgoing rays from the raindrop to the observer must be exactly 42 degrees. 

The students asked why rainbows form arcs and not just a "sheet of colors". The term Solid Angle was introduced them to explain that the 42 degree constraint on the rainbow must be roated, wich is responsble for the arc. If there was no horizon, the rainbow would appear to be a full circle whose radius depends on the distance between the observer and the raindrops.