how rainbow is formed in the sky

Atmospheric Optics and Refraction

The phenomenon of a spectral arc appearing in the sky is a result of the interaction of sunlight with water droplets suspended in the atmosphere.

The Role of Light Refraction

Sunlight is composed of a spectrum of colors. When sunlight enters a water droplet, it slows down and bends (refracts) due to the change in density between air and water. The degree of bending differs depending on the wavelength of light; shorter wavelengths (violet and blue) bend more sharply than longer wavelengths (red and orange).

Internal Reflection and Dispersion

Once inside the droplet, the light undergoes internal reflection off the back inner surface of the droplet. This reflection further separates the wavelengths, enhancing the dispersion of colors. The light then exits the droplet, having been refracted a second time, resulting in a separation of the spectrum into distinct bands of color.

Observation and Geometry

To observe the spectral arc, the sun must be behind the observer, and the water droplets must be at a specific angle (approximately 42 degrees) relative to the observer's line of sight. The position of the arc is therefore relative to the observer and the sun.

Factors Affecting Visibility

  • Water Droplet Size and Density: The size and distribution of water droplets influence the brightness and sharpness of the arc. Larger, uniformly sized droplets produce brighter, sharper arcs.
  • Sunlight Intensity: The intensity of sunlight impacts the overall brightness of the arc. Bright sunlight leads to a more vibrant arc.
  • Atmospheric Conditions: Clouds or haze can obscure or diminish the visibility of the arc.

Types of Arcs

Variations in atmospheric conditions and the angle of the sun can produce different types of arcs, including double arcs and supernumerary bows.

Related Phenomena

Similar optical phenomena, such as halos and glories, are also caused by the interaction of light with atmospheric particles, although they involve different physical mechanisms.