Minimum angle of deviation

The minimum angle of deviation of a ray of light of any specific wavelength passing through a raindrop is the smallest angle to which it must change course before it becomes visible within the arcs of a rainbow to an observer.

Remember that:
  • Any ray of light (stream of photons) travelling through empty space, unaffected by gravitational forces, travels in a straight line forever.
  • When light travels from a vacuum or from one transparent medium into another, it deviates from its original path (and changes speed).
  • The more a ray changes direction the greater its angle of deviation.
  • A ray reflected directly back on itself has an angle of deviation of 1800 – the maximum possible angle of deviation.
  • It is the optical properties of air and raindrops that determines the angle of deviation of any ray of incident light.
  • It is the optical properties of raindrops that prevent any ray of visible light within the visible spectrum from exiting a raindrop towards an observer at an angle of deviation less than 137.60.
  • The angle of deviation and the angle of deflection are directly related to one another and together always add up to 1800.
  • The angle of deviation and the viewing angle are always the same.
More about the minimum angle of deviation
  • The optical properties of an idealised spherical raindrop mean that no light of any particular wavelength can deviate at less than its minimum angle of deviation.
  • The minimum angle of deviation of visible light depends on its wavelength.
  • The minimum angle of deviation for red light with a wavelength of approx. 720 nm is 137.60 but similar rays of the same wavelength but with other impact parameters can deviate up to a maximum of 1800.
  • Different colours have different minimum angles of deviation because the refractive index of water changes with wavelength.
Impact parameter and minimum angle of deviation
  • To form a primary rainbow, incident light must strike each raindrop above its horizontal axis.
  • Rays of incident light of a single wavelength strike a raindrop at every possible point on the side of a raindrop facing the Sun.
  • Only those that strike above the horizontal axis contribute to a primary rainbow.
  • Points of impact of incident light striking a droplet can be measured on an impact parameter scale.
  • It is the point of impact of rays of incident light of the same wavelength that is the variable factor that determines their subsequently different paths.
  • Rays that strike nearest the horizontal axis, so with a value near 0.0 on an impact parameter scale have the largest angles of deviation.
  • Rays that strike farthest away from the horizontal axis (near the topmost point on an impact parameter scale and so near 1.0) also have a large angle of deviation.