Wonders of the Universe - Brian Cox [24]
The first scientific explanation, which pre-dated Newton by several decades, was given by René Descartes in 1637. Water droplets in the air are essentially little spheres of water, so Descartes considered what happens to a single ray of light from the Sun as it enters a single water droplet. As the diagram opposite illustrates, the light ray from the Sun (S) enters the face of the droplet and is bent slightly. This is known as refraction; light gets deflected when it crosses a boundary between two different substances (point A), then when the light ray gets to the back surface of the raindrop, it is reflected back into the raindrop (point B), finally emerging out of the front again, where it gets bent a little more (point C). The light ray then travels from the raindrop to your eye (E).
The key point is that there is a maximum angle (D) through which light that enters the raindrop gets bounced back. Descartes calculated this angle for red light and found it to be forty-two degrees. For blue light, the angle is forty degrees. Colours between blue and red in the spectrum have maximum angles of reflection of between forty-two and forty degrees. No light gets bounced back with angles greater than this, and it turns out that most of the light gets reflected back at this special, maximum angle. So, here is the explanation for the rainbow. When you look up at a rainbow, imagine drawing a line between the Sun, which must be behind you, through your head and onto the ground in front of you. At an angle of forty-two degrees to this line, you’ll see the so-called rainbow, or Descartes’ ray of red light. At an angle of forty degrees to this line, you’ll see the Descartes’ ray of blue light, and all the colours of the rainbow in between. There is some light reflected back to your eye through shallower angles, which is why the sky is brighter below the arc than above it. You don’t see the colours below the arc because all the rays merge to form white light. On the picture on the previous page, you can see the sky brightening inside the rainbow over the Victoria Falls, and the relative darkness of the sky outside it.
So raindrops separate the white sunlight into a rainbow because each of the consituent colours gets reflected back to your eye at a slightly different maximum angle. But why the arc? In fact, rainbows are circular. Think of the imaginary line again between the Sun, your head and the ground. There isn’t just one place at which the angle between this line and the sky is forty-two degrees, there is a whole circle of points surrounding the line. The reason you can’t see a complete circle is that the horizon cuts it off, so you only see the arc. This is also why you tend to see rainbows in the early morning or late afternoon. As the Sun climbs in the sky, the line between the Sun and your head steepens and the rainbow, which is centred on this line, drops closer and closer to the horizon until at some point it will vanish below the horizon.
All the way back to Aristotle, scientists have been trying to understand rainbows and how white light is transformed to colour through this medium. The Victoria Falls are perhaps one of the most spectacular places on Earth to see rainbows; here, these features hover in the sky above the cascading waters whenever the Sun shines through the mist.
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THE ELECTROMAGNETIC SPECTRUM
The electromagnetic spectrum is composed of a range of wavelengths from radio waves at the very longest end to gamma rays at the shortest. Our eyes are sensitive to a limited range in the middle which we know as visible light.
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In fact, rainbows are circular. The reason you can’t see a complete circle is that the horizon cuts it off, so you only see the arc. This is also why you tend to see rainbows in the early morning or late afternoon.
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WHAT MAKES A RAINBOW AN ARC?
Decartes’ theory was based on what happens to a single ray of light from the Sun as it enters a water droplet; he discovered that each colour that makes up this light is refracted,