Q.(i) State the conditions under which a rainbow can be seen.

[!TLDR] Rain plus low morning/evening Sun gives a primary bow (one internal reflection, red outer, ~41-43 degrees) and, more rarely, a secondary bow (two reflections, violet outer, ~51-53 degrees) simultaneously, both centred on the anti-solar point. [!ANSWER] (i) Rain + enough sunlight + Sun low in the sky.

(ii) Primary: one internal reflection, red outer ~41-43 degrees. …

1. A rainbow requires: a light shower of relatively large raindrops (not too small, else diffraction dominates and washes out the colours), morning or evening timing (so the Sun is low enough in the sky for the visible angular band to lie above the horizon), and enough sunlight intensity to see the resulting colours clearly.
2. The PRIMARY rainbow forms when sunlight enters the UPPER portion of a spherical raindrop, refracts and disperses into its constituent colours, undergoes exactly ONE internal reflection (partial, never total, since the internal angle never reaches the water-air critical angle) off the drop's far inner surface, and refracts a second time on finally exiting. The two extreme colours emerge inclined to the horizontal ground level at about 43 degrees (red) and about 41 degrees (violet), so red appears on the OUTER edge of the visible arch and violet on the inner edge; it is visible within the angular range of about 41 to 43 degrees from the horizontal (measured from the anti-solar point).
3. The SECONDARY rainbow forms from sunlight entering the LOWER portion of a raindrop, undergoing TWO successive internal reflections before finally emerging, at larger angles of about 51 degrees (red) and 53 degrees (violet) from the horizontal -- reversing the colour order (violet now outer, red inner) and lying at a wider angle (hence appearing OUTSIDE the primary bow); it is fainter, since each additional internal reflection loses more light. It is visible within roughly 51 to 53 degrees from the horizontal. …

Address each of the four sub-parts in turn: state the three joint conditions, describe the primary bow's single-reflection geometry and angular range, describe the secondary bow's double-reflection geometry and angular …

Reversing which bow has red outer versus violet outer (primary=red outer, secondary=violet outer -- the two are opposite), or omitting the specific angular ra …