NDA (II) 2017 General Ability Test · Question 125 of 150

Correct — A, Dispersion of light. Sunlight entering a raindrop is refracted at the front surface, reflected once off the back of the drop and refracted again as it leaves. Refraction and internal reflection steer the light, but the step that turns white sunlight into a band of colours is dispersion: the refractive index of water is slightly different for each wavelength, so violet is bent more than red and the colours emerge along slightly different directions. Only that separation makes a bow rather than a bright arc of white light, which is why the key names dispersion. The most intense returning light leaves at about 42 degrees from the point directly opposite the Sun, and that angle is what fixes the size of the arc.

• (b)Interference of light — Interference does appear in the sky, but only in the faint extra bands sometimes seen just inside the main bow, called supernumerary bows. It plays no part in producing the ordinary rainbow itself.
• (c)Diffraction of light — Diffraction is the bending of light around obstacles and through narrow openings. It gives the coloured rings of a corona around the Moon and the colours on a compact disc, but a raindrop is far too large for diffraction to shape a rainbow.
• (d)Scattering of light by atmospheric dust — Scattering explains the blue of the sky and the red of sunrise and sunset, where short wavelengths are scattered out of the beam. A rainbow needs actual water drops and a definite geometry, not dust.

Dispersion is the splitting of white light into its constituent colours because the refractive index of a medium varies with wavelength. Newton demonstrated it with a glass prism, and a raindrop does the same work with two refractions and a reflection in between. Violet, having the shortest wavelength of the visible band, meets the highest refractive index and is deviated most; red is deviated least. In the primary bow that ordering puts red on the outer edge and violet on the inner one.

Two geometric facts make a rainbow easy to recognise in a question. It always appears in the part of the sky opposite the Sun, centred on the antisolar point, which is why you see one with the Sun behind you and rain ahead. And the bright arc sits at roughly 42 degrees from that centre. A secondary bow, formed by two internal reflections instead of one, appears higher up, is fainter, and has its colours reversed. Keep the four optical phenomena separate by their signature effects: dispersion for the rainbow and the prism, scattering for the blue sky and red sunset, total internal reflection for the desert mirage and the optical fibre, and diffraction or interference for coronas, thin-film colours and supernumerary bands.

• A rainbow forms by refraction on entry, dispersion into colours, one internal reflection at the back of the drop, and refraction again on exit.
• The most intense returning light emerges at about 42 degrees from the antisolar point, which sets the radius of the primary bow.
• Blue and violet are bent more than red, so red lies on the outer edge of the primary bow.
• The secondary bow involves two internal reflections, is fainter, sits outside the primary and has its colour order reversed.
• Interference accounts only for the faint supernumerary bows, and diffraction is not the cause of a rainbow at all.

• Choosing scattering because it is the phenomenon behind the sky's colour; a rainbow needs drops and geometry.
• Reading interference as the cause of the main bow rather than of the faint supernumerary bands.
• Forgetting that a rainbow always lies opposite the Sun, so it cannot be seen when looking towards it.

NDA asks which optical phenomenon explains a named sight — a rainbow, a mirage, a red sunset, a twinkling star or a lemon in a tumbler.

• practice — not a real PYQ

  In the primary rainbow, the colour seen on the outer edge of the arc is

  • (a)violet
  • (b)green
  • (c)red
  • (d)blue

  Answer(c) red — red is bent least on refraction, so it emerges at the larger angle and lies on the outside of the bow.

• practice — not a real PYQ

  The blue colour of the clear sky is due to

  • (a)dispersion of sunlight
  • (b)scattering of sunlight by air molecules
  • (c)total internal reflection in the atmosphere
  • (d)interference of sunlight

  Answer(b) scattering of sunlight by air molecules — shorter wavelengths are scattered far more strongly, which is a different phenomenon from the one that makes a rainbow.