“A rainbow is the combined effect of the refraction, dispersion and total internal reflection of light.” Prove this statement with the help of diagram and explain it.

Answer: Sunlight entering a raindrop is refracted and dispersed, totally internally reflected at the back of the drop, and refracted again as it comes out — these three effects together produce the rainbow.

Diagram (formation of a rainbow in a water droplet):

   white sunlight
  ------------------>*  (1) refraction + dispersion
                    / \      at entry into the drop
          .-------/---\-----.
        /       /       \     \
       |      /    drop   \    |
       |    /  (water)      \  |
       |   / violet     red  \ |
        \  \                 / *  (2) total internal
         '--\-------------- /-'      reflection at the
             \  (3) refraction       back surface
              \  at exit   /
               v          v
            violet       red
                 \       /
                  observer's eye
          (sun is behind the observer)

Labels: incident white light; raindrop; refraction and dispersion at entry; total internal reflection at the inner (back) surface; refraction at exit; red and violet emergent rays; observer.

Explanation:

• Refraction: after rain, tiny spherical water droplets remain suspended in the air. A ray of sunlight entering a droplet passes from air (rarer) into water (denser) and bends towards the normal; on leaving it bends away from the normal.
• Dispersion: the refractive index of water is different for different colours, so each colour bends by a different amount — violet the most and red the least. The white light therefore splits into its seven colours (VIBGYOR) inside the droplet.
• Total internal reflection: the coloured rays strike the inner back surface of the droplet at an angle greater than the critical angle, so they are totally reflected back into the droplet instead of passing out.

The rays then refract again at the front surface and emerge at different angles (red at about 42º and violet at about 40º to the incident sunlight). Light of different colours from many droplets reaches the eye, and we see an arc of seven colours — red on the outer side and violet on the inner side. A rainbow is seen only when the sun is behind the observer. Thus the rainbow is the combined effect of refraction, dispersion and total internal reflection of light.