# Romantic reverie explores beauty of sky

I WAS walking through St Stephen's Green last week and passed by a particular seat that struck a chord of memory. Many years ago, when I was a postgraduate student, I sat on that seat with my girlfriend (now my wife) on a warm summer afternoon. I asked her if she knew why the sky is blue.

I guessed (correctly) that she wouldn't know the answer, and I wanted to impress her with my great command of interesting information. I now propose to attempt to impress a much wider audience, and as a bonus I will throw in an explanation of the rainbow.

In a nutshell, the blue colour of the sky is caused by the scattering of light and the spectrum of colours in the rainbow is caused by refraction (bending) of light. Ordinary daylight (white light) is in fact a mixture of seven different coloured lights. When the seven different colours are jumbled together the mixture is colourless.

The different colours can be separated from each other, and thereby revealed, by passing white light through a glass prism, as first clearly demonstrated by Isaac Newton. The physical nature of light is that of a wave. Different waves can be characterised by their wavelengths - the distance from one wave peak to the next peak. Each of the colours in white light has its own characteristic wavelength.

The reason the sky is blue can be illustrated by carrying out a simple experiment. For this you will require a glass bowl (e.g. a fish bowl), a flashlamp and some milk. Almost fill the bowl with water and now stir a little milk into the water. The light from the bulb in the flashlamp will either be almost colourless, or else have a slight yellow tinge. Now look at the bulb head on through the milky water. The light will look markedly reddened, and from the side the milky water will have a blue hue.

Scattering of light explains the results of the experiment. Some of the light that enters the bowl passes straight through, but some is scattered in all directions by the tiny milk particles. The milk droplets are better at scattering blue light than other colours, which explains the blue colour from the side. The light that passes through the bowl appears reddened because it has been depleted of its blue colour by scattering.

Scattering of light also explains the blue colour of the sky - the atmosphere scatters the blue component of the sun's white light. When the sun is directly overhead its light passes through a relatively small thickness of atmosphere and not much blue light is scattered.

On the other hand, at sunset the light travels obliquely through much more atmosphere, much more blue lights is scattered out and the setting sun will be coloured. The precise hue of the colour will depend on how much dust is present in the atmosphere, and can range anywhere from faint orange to bright red. Reflection of coloured light from the setting sun off clouds can yield spectacularly beautiful sights.

The moon has no atmosphere to scatter light. The sky as seen from the moon is always black, even when the sun is in the sky. Shadows on the moon are intensely black and sharp edged. If you stood on the moon and looked towards the Earth you would see our beautiful globe floating on the black background of space. The Earth is blue coloured because the atmosphere scatters the blue light and you will also see fleecy white clouds.

After a rain shower, when the sun breaks out, if you quickly look the other way you will see a rainbow in the direction opposite the sun. If you observe from an aircraft you will see the rainbow as a perfect circle. Observed from the ground, part of the circle is always under the horizon.

The most brilliant colour in the bow, found at the uppermost edge, is red, followed in descending order of brightness by orange, yellow, green, blue, indigo and violet. (The spectrum of colours can be easily recalled by remembering the name Roy G. Biv.)

Sometimes you can also see a second rainbow higher in the sky. The second rainbow has a reversed order of colours to the first. The sky between the two rainbows is distinctly darker than the rest of the sky.

The rainbow always appears as a perfect semi circle to observers on the ground. If an observer moves a distance and looks again, the rainbow continues to appear as a perfect semi circle. This shows that the rainbow is not a tangible object in the sky. If it were it would change shape depending on the angle of observation.

Each observer sees his/her own rainbow which is an image in the eye that moves with the observer and doesn't change shape. Since the rainbow is not really an object it can never be caught and its ends remain forever elusive - there is no way you can ever get to that crock of gold and its guardian leprechaun.

The rainbow effect is produced by the action of individual raindrops on sunlight and the shape of the rainbow is determined by the geometrical relationship between the sun, the raindrop and the eye.

When sunlight enters the raindrop it is bent, reflected from the concave back of the drop and bent again as it leaves the front. The different colours in the white light are each bent by slightly different amounts so that the light that emerges is splayed into the spectrum of seven colours.

The colours can be seen, however, only when the angle of reflection between the sun, the drop of water and the observer's line of vision is between 400 and 420 (see illustration). The rainbow has to be circular because only a circle ensures that the geometrical relation between the sun, an observer and a point on the rainbow is the same for every point. When the sun is more than 420 above the horizon a rainbow cannot be seen because the required angle passes over the head of the observer.

The secondary rainbow, often too faint to be seen, is explained by the fact that sometimes light entering the raindrop undergoes a double internal reflection before re emerging.

Finally, let me say that when I look up at a clear blue sky or behold a fine example of a rainbow, my mind doesn't automatically switch to considerations of the scattering or the refraction of light. I will feel something like `Isn't that beautiful', or `God, it's good to be alive', or I may think of that seat in St Stephen's Green. The beauty of the world and its emotional effect on us is a reality as valid as understanding the underlying physical basis of the appearance. But isn't it nice to be able to understand things in several different ways?