CDS (I) 2021 General Knowledge · Question 117 of 120

Correct — B, 1. A primary rainbow is made by light that undergoes exactly one internal reflection inside each raindrop. Sunlight enters the drop and is refracted at the surface; the refractive index of water is slightly different for each wavelength, so the colours separate as they bend — that is dispersion. The separated light travels to the far side of the drop, where part of it is reflected once off the inside surface, and it then leaves through the front, refracting a second time. The rays emerge most intensely at about 42 degrees from the direction opposite the Sun, which is why the bow is an arc at a fixed angle and why it has red on the outside. Refraction, dispersion, one internal reflection, refraction — that is the whole primary bow.

• (a)0 — With no internal reflection the light would simply pass through the drop and carry on away from the observer. Something has to turn it back towards the eye, and the reflection off the rear inner surface is what does it.
• (c)2 — Two internal reflections make the secondary rainbow — the fainter outer bow at about 50 to 53 degrees, whose colour order is reversed with red on the inside. It exists, but it is not the primary bow.
• (d)More than 2 — Higher-order bows are possible in principle, but each extra reflection loses light and they are far too faint to be seen against the daytime sky.

A rainbow is the combined output of millions of raindrops, each acting as a tiny prism and mirror. Refraction bends the light on entering and leaving; dispersion separates the colours, because blue is bent more than red; and internal reflection sends the light back towards an observer standing with the Sun behind them. The number of internal reflections fixes which bow is being seen and at what angle it appears.

The item can be settled by remembering the pair rather than the single figure — one reflection gives the bright primary bow, two give the faint secondary. The reversed colour order of the secondary is the check: an extra reflection turns the sequence round, so red sits outside on the primary and inside on the secondary. Option (a) is worth thinking through rather than dismissing, because it makes clear why a reflection is needed at all: without one, no light would come back to the observer's eye and there would be nothing to see. Two related facts are often asked alongside — the bow is always seen with the Sun behind the observer, and dispersion is the step that produces the colours.

• The primary rainbow involves refraction on entry, dispersion, one internal reflection and refraction on exit.
• The primary bow appears at about 42 degrees from the point opposite the Sun, with red on the outer edge.
• The secondary bow comes from two internal reflections, appears at about 50 to 53 degrees, is fainter, and has its colours reversed.
• Dispersion happens because the refractive index of water varies slightly with wavelength.
• A rainbow is always seen in the part of the sky opposite the Sun, so the observer has the Sun behind them.

• Answering two, which is the count for the secondary bow rather than the primary.
• Treating the rainbow as scattering, which explains the blue sky rather than the bow.
• Forgetting that refraction happens twice, on entering and on leaving the drop.

As this count of reflections, as a which-phenomena-are-involved statement set, or as a comparison of the primary and secondary bows.

• practice — not a real PYQ

  The secondary rainbow differs from the primary rainbow in that it

  • (a)involves no internal reflection
  • (b)involves two internal reflections and has its colours reversed
  • (c)is always brighter
  • (d)appears on the same side of the sky as the Sun

  Answer(b) involves two internal reflections and has its colours reversed — the extra reflection turns the colour order round and loses light, so the outer bow is fainter with red on the inside.

• practice — not a real PYQ

  The separation of white light into its colours as it passes through a raindrop is called

  • (a)reflection
  • (b)dispersion
  • (c)diffraction
  • (d)scattering

  Answer(b) dispersion — the refractive index of water is slightly different for each wavelength, so the colours bend by different amounts and fan out.