Laws of refraction and reflection

The path of light through a raindrop is a key factor in determining whether it will direct light towards an observer and contribute to their perception of a rainbow. This can be broken down as follows:

  • The impact parameter is a measure of the direction from which rays of incident light approach a raindrop and the point at which they strike the surface.
  • When using a ray-tracing diagram to map the path of rays through a raindrop, an impact parameter scale is used to select which incident rays are of interest.
  • An impact parameter scale is aligned with parallel incident rays and divides the relevant part of the surface of a droplet into equal parts.
  • Using a scale with steps between zero and one, 0 is aligned with the ray that passes through the centre of a droplet and 1 with the ray that grazes the surface without refraction or reflection.
Remember that:
  • Primary rainbows form when incident light strikes raindrops above their horizontal axis reflecting once off the inside before exiting towards an observer.
  • Incident light that strikes raindrops below their horizontal axis and reflects once on the inside before exiting, directs light upwards away from an observer.
  • Secondary rainbows form when incident light strikes raindrops below their horizontal axis reflecting twice off the inside before exiting downwards.
  • The Law of reflection deals with the angles of incidence and reflection when light strikes and bounces back off a surface and can be used for calculations relating to the curved surfaces of a raindrop.
  • Remember that the law of reflection states that the angle of incidence always equals the angle of reflection for a mirror-like (specular) surface.
  • The Law of Refraction (Snell’s law) deals with the changes in the speed and direction of incident light as it crosses the boundaries between air and a raindrop and then between a raindrop and the surrounding air.
  • An equation can be derived from Snell’s law that deals with the relationship between the angle of incidence and the angle of refraction of light with reference to the refractive indices of both media.