One afternoon I turned on an incandescent lamp and noticed that an object's shadow was blue. I conducted some more experiments and found that the phenomenon only happened when sunlight was combined with the light from the incandescent lamp. I then tried lamps of many colours, with the results shown below. Coloured shadows are a well-known optical phenomenon, although most people do not follow them up as carefully as your correspondent. The colours of the rainbow are created by all visible wavelengths, including that for violet and red.
White light consists of a mixture of all the wavelengths in the right proportions.
The eye contains three kinds of colour photoreceptors, known as cones, which are sensitive to different wavelengths of visible light. The three types of cones have their highest sensitivity in the blue, green and red regions of the spectrum respectively. Each visible colour produces a unique combination of sensory signals from the different cones. In addition, the brain does a lot of image processing, so the colour perceived depends not only on its actual wavelength spectrum but also on its surroundings. In particular, if an area is illuminated with a broad range of wavelengths, the eye will tend to see the illumination as white.