Rainbows

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

The photos below show rainbows.  You know from your experiments in labs 2 and 3 that prisms can separate white light in to 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 by a different amount.  As we saw in a class demo violet is bent the most and red the least.  But what is the sky could act as a prism?

Figure 1.  Rainbow with all colors, ROY G BV.  Notice that violet is on the inside and the red along the outside of the bow.  Also seen is a somewhat rare 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 little 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 passed into the water droplet?  Try to predict the path of the light and each colored component before reading on.  Of course the drawing is not to scale, the size of the droplet is greatly exaggerated.

Figure 2.  Close-up of the bow, again with blue on the inside.

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

The path of the red ray show 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.  As you can see the 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 were this water droplet is located.

What happens to the blue ray that entered at the same spot 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 leads to the situation shown above.  The blue ray from the water droplet goes over the persons head and they never see the blue ray!  This means they never see blue coming from the region of the sky were 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 persons head as well.  The angle between the incoming white  Sun ray and the outgoing red ray is about 42o.

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, 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 there light in a direction that our observer can see.  The blue light from these same droplets will pass over the observers 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 then the droplets that he sees the red 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 and so he sees no red coming from that region of the sky.  The result is he see 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 3.  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 prism it strikes the back wall and reflects.  As the reflected ray travels through the prism 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 4.  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 5.  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.

Water

Droplets

in the

Sky

Light Rays from Sun

copyright Marcus Milling  2009