Rainbows

How do rainbows form?  Is reflection or refraction important in their formation?

The photos below show rainbows.  You know from your experiments in Labs 2 and 3 that prisms can separate white light into its components, which we often abbreviate ROY G BV.  This happens because as light refracts into a more dense material (the glass prism), each color is bent at a slightly different angle.  As we saw in a class demonstration, violet is bent the most and red the least.  But how does the sky act as a prism?

Figure 1,  The picture shows a rainbow with all colors, ROY G BV.  Notice that violet is on the inside and red along the outside of the bow.  Also seen is a rare and somewhat less bright double rainbow, where the colors are reversed, with red on the inside.

After a rain, very small water droplets can hang in the air for an extended period of time.  These droplets can act as many tiny prisms.  On the diagram below, some of these droplets are shown along with light from the sun striking one of the droplets.  What will happen to the light as it passes into the water droplet?  Try to predict the path of the light and specifically, each colored component before reading on.  Of course the drawing is not to scale. The size of the droplet is greatly exaggerated.

Figure 2,  The picture shows a close-up of the bow, again with violet on the inside.

Figure 3,  When a light ray from the Sun strikes a water droplet, what happens?  Draw the normal line at the strike-point to help predict the results.

The path of the red ray shown above should have been predictable based on the experiments you have done in class (Labs 1 and 2).  An angle table, similar to the one you have for green rays, can be used to accurately draw the angles for both red ray refractions. The angle between the incoming white sun ray and the outgoing red ray is about 42o. As you can see, the red ray enters the eye of someone standing on the ground and they see the red part of the rainbow coming from the region of the sky where this water droplet is located.

What happens to the blue ray that entered the water droplet at the same point as the red ray?

As the blue light ray travels through the prism, it refracts twice, just like the red ray, but each time it bends more than the red ray.  This refraction leads to the situation shown above.  The blue ray from the water droplet goes over the person’s head and they never see that blue ray!  This means they do not see blue coming from the region of the sky where this droplet is located.  Since the orange, yellow, and green travel between the red and blue rays, the orange, yellow and green rays from this droplet go over the person’s head as well.

If the person is only seeing red at this point, how do they see the whole rainbow?

Remember from what we saw on the diagrams above that the red and blue rays refract and reflect as they move from the air, through the droplets, and back out into the air.  This causes the red rays from certain droplets to send the light in a direction that our observer can see.  The blue light from these same droplets will pass over our observer’s head (along with the orange, yellow, and green) and will not be seen by our observer.

The observer sees the blue rays coming from droplets that are lower in the sky than the droplets that he sees the red rays coming from.  The droplets from which he sees the blue rays coming from are also reflecting red light toward him but these red rays pass under the level of his eyes so he does not see red coming from that region of the sky.  The result is he sees red coming from a higher region of the sky, and sees blue coming from a lower region of the sky, with orange, yellow, and green coming from the regions in between these extremes.

For an even bigger challenge, try and explain where the second rainbow, in the double rainbow, comes from.  You have all the knowledge you need from your lab experiments, you just have to apply it in a creative way to the water droplets!

Sun

Water

Droplet

As the ray refracts into the water droplet, what happens as it hits the back side?

Figure 4,  When the light ray from the sun strikes the water droplet, the red ray refracts into the droplet, bending toward the normal.  As the refracted ray travels through the droplet, it strikes the back wall and reflects.  As the reflected ray travels through the water droplet, it strikes the front of the droplet and refracts into the air, bending away from the normal.  Note: Drawing, obviously, not to scale.

Water

Droplet

Light Ray from Sun

Figure 5,  When the light ray from the Sun strikes the water droplet, the blue ray refracts into the droplet, bending toward the normal, but bending more than the red ray.  As the refracted blue ray travels through the prism it strikes the back wall and reflects.  As the reflected blue ray travels through the prism, it strikes the front of the droplet and refracts into the air, bending away from the normal, but bending more than the red ray.  Note: Drawing, obviously, not to scale.

Water

Droplet

Light Ray from Sun

Figure 6,  Light rays coming from the sun hit all the water droplets hanging in the air after a rain.  This is how the different colors of the rainbow are seen coming from different parts of the sky.  The black arrows represent white light coming from the Sun.

Water

Droplets

in the

Sky

Light Rays from Sun

Copyright  © 2009-2012, by Marcus Milling

edited by Julia Pian