## Light and Color

### Water drop

The following figure represents a cut of a drop of water through a plane with an incident ray and the ray paths in which that incident ray unfolds. As it is a simpler case, we will initially consider the horizontal incident ray, coming from the left and with a color corresponding to a given frequency and a given index of refraction.

The ray, when it hits the drop at a point $$P_{1}$$, emits two rays, one $$C_{1}$$, reflecting towards the outside and the other obtained by refraction, inside the drop, uniting $$P_{1}$$ to another point $$P_{2}$$. Once there, a part of the ray refracts, this time to the outside in a ray $$C_{2}$$ of origin $$P_{2}$$ and another is reflected at $$P_{2}$$ on the tangent to the edge of the drop, until it reaches the point $$P_{3}$$ and there again it subdivides into a ray refracted outwards $$C_{3}$$ and another reflected $$P_{3}P{4 }$$, which refracts on a $$C_{4}$$ to the outside. Of course, in each of these subdivisions of a ray into a reflected and a refracted one, there is a loss of intensity for each of the results. It is therefore natural to start by observing the possible contribution of the first four rays emerging from this drop - $$C_{1}$$, $$C_{2}$$, $$C_{3}$$, $$C_{ 4}$$ - for any relevant luminous phenomenon observable in the sky. Now, these 4 rays all depend on the point of impact of the ray incident on the drop (the point $$P_{1}$$), which can be parameterized by the ordinate of $$P_{1}$$, varying between $$-r$$ and $$r$$, if we call the radius of the drop $$r$$.

• In the following interactive application you can vary the impact point and the color of the incident ray and analyze that variation in the path of the rays $$C_{1}$$, $$C_{2}$$, $$C_{3}$$ and $$C_{4}$$.