A rainbow from a hose

You need: a garden hose with a spray nozzle (or a spray bottle), a sunny day, and a sun that is low in the sky: morning or late afternoon.

You need: a hose with a spray nozzle, a sunny day, and a low sun (morning or late afternoon).

Hose; low sun, height $s<42^{\circ }$.

Stand with your back to the sun. Spray a fine mist in front of you and away from you, at the height of your face. Look where the head of your own shadow points: the rainbow is a circle around that spot.

Back to the sun, spray a fine mist in front of you. The rainbow is a circle around the point opposite the sun, where the head of your shadow points.

Back to the sun; centre $A$ opposite it.

The circle has a radius of forty-two degrees, as seen from your eye. Red is on the outside at forty-two degrees, violet on the inside at forty. Hold out your arm: your open hand covers about twenty degrees, so the red edge is about two hands from the centre.

Radius: red $42^{\circ }$ (outside), violet $40^{\circ }$ (inside). An open hand at arm's length is $d\approx 20^{\circ }$, so red is $42/20\approx 2$ hands from the centre.

Red $r_R=42^{\circ }$, violet $r_V=40^{\circ }$, open hand $d\approx 20^{\circ }$, $42/20\approx 2$ hands.

In the sky, the top of the rainbow is forty-two degrees minus the height of the sun. With the sun twenty degrees high, the top is twenty-two degrees up. With the sun forty-two degrees high or more, the top is on the ground or below it, and there is no rainbow in the sky.

Top of the bow: $h=42^{\circ }-s$, where $s$ is the sun's height. If $s=20^{\circ }$ then $h=22^{\circ }$. If $s\ge 42^{\circ }$ then $h\le 0^{\circ }$: no rainbow in the sky.

Top $h=42^{\circ }-s$; $s=20^{\circ }\Rightarrow h=22^{\circ }$; $s\ge 42^{\circ }\Rightarrow h\le 0^{\circ }$.