Rainbow Formation - UNSOLVED PRACTICE SET

Q7. Explain the three optical phenomena that combine to produce a rainbow.

Q8. Why is a rainbow always seen in the direction opposite to the Sun? What must the conditions be for a rainbow to appear?

Q9. Describe the colour arrangement in a primary rainbow. Which colour is on the outside (top) and which is on the inside (bottom)? Why?

Q10. What is a secondary rainbow? How does it differ from a primary rainbow in terms of:
(a) colour order,
(b) brightness, and
(c) number of internal reflections?

Q11. Why can we never see a rainbow at midday when the Sun is directly overhead? Explain in terms of the geometry of rainbow formation.

Q12. Can rainbows be seen at night? Explain. Can rainbows be formed artificially? Describe one way to create a rainbow indoors.

Q13. Describe the formation of a primary rainbow in detail. Your answer must cover:
(a) the entry of sunlight into a spherical raindrop and the first refraction (with dispersion),
(b) the internal reflection at the back of the drop,
(c) the second refraction as light exits the drop (with further dispersion),
(d) why different colours exit at different angles (red at ~42°, violet at ~40° from the anti-solar point), and
(e) how the observer's eye receives different colours from drops at different positions in the sky.

Q14. Compare primary and secondary rainbows in detail:
(a) the number of internal reflections in each,
(b) the colour arrangement in each (which colour is on top),
(c) the angular radius of each (primary ~42°, secondary ~51°),
(d) why the secondary rainbow is always dimmer than the primary,
(e) what is the 'dark band' (Alexander's band) between the two rainbows, and explain why that region appears darker.

Q15. Analyse the conditions necessary to see a rainbow and explain why they must all be met simultaneously. Your answer should cover:
(a) the presence of water droplets acting as dispersive prisms in the atmosphere,
(b) the need for sunlight from behind the observer,
(c) the anti-solar point and the cone of coloured light from each raindrop,
(d) why the rainbow appears as an arc and not a full circle (horizon cuts it),
(e) a practical Indian context: explain when and where rainbows are most commonly seen in India (monsoon season, morning, evening, etc.) and why.

Q16. The critical angle for water is approximately 48°.
(a) Calculate the refractive index of water using n = 1/sin C.
(b) Sunlight enters a spherical raindrop at an angle of incidence of 60°. Using n_water = 1.33 and Snell's Law, find the angle of refraction inside the drop.
(c) Does total internal reflection occur at the back of the drop if the angle of incidence there equals the refracted angle from (b)? Justify using the critical angle. (sin 60° = 0.866)

Q17. In a primary rainbow, red light exits raindrops at an angle of 42° from the anti-solar point, and violet light exits at 40°.
(a) What is the angular width of the primary rainbow spectrum?
(b) The observer is at point O and the anti-solar point is directly opposite the Sun. If the Sun is 3° above the horizon, at what elevation angle above the horizon does:
 (i) the red arc appear?
 (ii) the violet arc appear?
(c) At what time of day would a rainbow be highest in the sky and why?

Q18. A student creates an artificial 'rainbow' using a garden hose in sunlight in her Mumbai home garden.
(a) What must she ensure about the position of the Sun relative to herself and the spray?
(b) The spray droplets have diameter 1 mm. Does the same physics apply as for natural raindrops? Explain.
(c) The student notices the colours appear in the same VIBGYOR order as a natural rainbow. Explain why this happens using refraction and dispersion.
(d) If she increases the spray angle, does the rainbow arc move up or down? Explain.