A glorious scene imaged by atmospheric optics expert Alistair Fraser (blog) in British Columbia, Canada.

The primary and secondary rainbows are separated by Alexanders Dark Band. The sky is characteristically bright inside the primary. Wave tilted water prevents the reflected primary and primary meeting at the horizon.

©Alistair Fraser, shown with permission

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How many colours are there in the rainbow?    An infinite number because there is a continuous gradation of colour (strictly, hue saturation and value or their equivalent) across it from red to violet.

How many colours can we actually see in a rainbow?  Our eyes have three types of colour sensor cones and collectively with brain processing they can distinguish some 2,000,000 or more different colour combinations.   Rather more than the traditional rainbow colours of redorangeyellow, greenblueindigoviolet !

Rainbow colours are not single wavelength spectral colours.   Unlike a prism, a raindrop disperses sunlight such that colours overlap.   Each particular angle of the rainbow has a main spectral colour that is overlapped by a weaker mixture of all other colours of longer wavelength.   Thus rainbow green is greens plus progressively weaker contributions of yellows, oranges and reds.

A simulated rainbow for drops 0.7mm diameter.
The final bow is the sum of contributions from all wavelengths - thousands in the Airy theory calculation that generated it rather than the 13 shown here. Composite bow intensities were weighted by the solar spectral intensity distribution at Earth's surface and were then convoluted over the angular diameter of the sun's disk.

Green is a mixture of greens plus some yellow and some reds - there is even a trace of blue there.

Supernumeraries are much higher contrast in monochromatic light - try it on a rainbow - but severe overlapping washes them out in white light.