Q.Between the primary and secondary rainbows, there is a dark band known as Alexandar's dark band. This is because

The primary rainbow (one internal reflection) sends light to the eye only at angles up to about $42^\circ$ from the antisolar point; the secondary rainbow (two internal reflections) only beyond about $51^\circ$. No droplet geometry produces a deviation that lands in between, so genuinely no light is scattered into that gap — it is not absorption (option c) and not destructive interference (option a, which actually explains the faint supernum …

Setting up

A rainbow is formed by sunlight entering spherical raindrops, reflecting once (primary) or twice (secondary) off the inner back surface, and refracting back out. For a given number of internal reflections, the deviation of a ray depends on where it strikes the droplet, and there is a minimum deviation angle at which rays bunch up and produce a bright, sharply-defined bow — this is the rainbow angle.

The primary bow (one internal reflection)

For red light with one internal reflection, the minimum deviation is about $138^\circ$. Measured from the antisolar point (the direction directly opposite the Sun, i.e. of your own shadow), the observed angular radius is

All the light this mechanism sends toward the eye lies at angles up to about $42^\circ$ from the antisolar point — never beyond.

The secondary bow (two internal reflections)

The extra reflection sends the light out at a larger deviation, about $129^\circ$ for red, giving an observed angular radius of

All the light this mechanism sends toward the eye lies at angles beyond about $51^\circ$.

The gap in between …

Method: Comparing Minimum-Deviation Angles to Locate a Rainbow's Angular Position

Use this method for any question about where a rainbow (or a related feature like Alexander's dark band) appears in the sky, or why a particular angular region is bright or dark.

Steps

Step 1: Recall the minimum-deviation angle for each number of internal reflections

Light forming the primary rainbow undergoes one internal reflection inside a raindrop, with a minimum deviation of roughly $138^\circ$ (for red light). Light forming the secondary rainbow undergoes two internal reflections, with a smaller minimum deviation of roughly $129^\circ$. Each additional internal reflection changes the minimum-deviation angle and (for the secondary bow) reverses the colour order.

Step 2: Convert deviation angle to the angle actually observed from the antisolar point

This gives roughly $42^\circ$ for the primary bow and roughly $51^\circ$ for the secondary bow (for red light in each case), measured from the point directly opposite the Sun.

Step 3: Compare the angular ranges each bow actually illuminates to find gaps or overlaps …