If sunlight is allowed to shine through a central hole in a piece of white cardboard and illuminate a spherical flask, a faint rainbow will appear on the cardboard. It has the shape of a closed circle and its angular distance is about 42 degrees, with red on the outside, as in a real rainbow. If the back side of the flask is painted with silver or aluminium paint, more of the light will be reflected and the rainbow should be brighter.
He suggests using a water-filled beaker that has a wrapping of a flexible mirror made from aluminized plastic film covering the back side so that no light is transmitted through the beaker. The light comes from a slide projector in which an opaque slide with a slit in it is inserted. The rainbow is seen on the screen. Bohren points out that it is bright on the inside of the bow from the refracted light inside the rarinbow angle.
Dr. Tom Arny, University of Massachusetts, has mentioned some of the items he uses to illustrate rainbows in his classroom laboratory. He writes
You can buy plastic spheres that illustrate how a rainbow forms fairly well.
Our physics demonstration laboratory also has some tiny glass beads from a reflective paint manufacturer that create a reasonable rainbow.
For classroom use, although a bit messy, you might get a small squirt plant mister. I've also used microscope slides glued edge to edge and stuck in plastacine to make a model ice crystal. Other demos are the simple pencil in a glass of water to show bending and light coming into the top of an aquarium and throwing a spectrum on the floor.