and the green flash are topics that we aren't always able to cover in
one of the class lectures. Or if we do it's on the Wednesday
before Thanksgiving or the Friday before Spring Break when a large
fraction of the students are absent (I usually cancel class the
Wednesday before Thanksgiving by the way). The
hope is that you the next time you see a rainbow or a mirage you might
spot some features that you might have otherwise overlooked. And
if you know where and when to look you might be fortunate enough to see
the green flash.
All three phenomena involve refraction which is the bending of
light as it passes from one transparent material into another. A
ray of light might travel from air into water, ice, or glass, for
When the light passes into a denser material (as shown above) the
light "bends toward the normal." The normal is the dotted line
shown above that is perpendicular to the boundary between the two
When the light travels from a dense material into a substance with
lower density, it "bends away from the normal."
The amount of bending depends on the wavelength or color of the
light. The shorter wavelengths (violet, blue, green) are
bent more than the longer wavelength colors (yellow, orange, and
Thus white light can be split into its colors as shown
The separation of white light into colors by refraction is called
This is what happens when you shine
light through a glass prism (the figure below is on p. 109
in the photocopied ClassNotes).
Here's a photograph of light
being split into
colors after passing
through a prism (the white light comes in from the right side of the
The figure above is a closeup view of a ray of white light
striking a spherical
raindrop. Some of the white light is reflected (a). The remainder
(b) enters the raindrop (only the red and violet rays are shown inside
the raindrop). This light is bent (refracted) and split
into colors (dispersed). Some of the colored rays of light
reflect off the back inside surface of the raindrop (c). The
colored rays of light emerge from the drop (where they are bend and
dispersed some more) and head back, more or less, in the direction they
came from (d). These are the rays you see in a rainbow.
Someone down at the ground (standing with
the sun at their back)
would see colored light coming from the raindrop. However because
each of the colors exits the drop at a slightly different angle (red
at 42o, violet at 40o, the other colors at angles
between 40o and 42o)
they would only see one of the coming from a given drop. They
see the ray that was headed straight toward their eyes. The other
rays would either pass above the person's head or strike the ground
The person would see red light
coming the drop A which is higher in the sky. They'd see violet
light coming from lower in the sky, from Drop B. The person would
see the other colors when they looked at the sky between A and B.
The next picture shows what the person on the ground would see.
light comes from the top edge of the rainbow, violet
from the lower edge. Blue, green, yellow, and
you'll see a faint secondary rainbow above the primary rainbow.
The following figure shows how this rainbow forms.
White light strikes the raindrop at a
position. The white light is again bent and separated into colors
but then is reflected twice
inside the raindrop before emerging on the
front side of the drop. An observer on the ground would need to
look 53o above the horizon to see the violet light and 50o
to see the
Here is a sketch showing both the primary
and the secondary
rainbow. The secondary rainbow is higher and dimmer than the
primary rainbow. The order of the colors in the secondary rainbow
is also reversed. Supernumerary arcs (faint bands of pink and
green) are sometimes visible below the primary rainbow (we won't go
into what produces the supernumerary arcs). Also the sky between
two rainbows appears darker than the rest of the sky (we won't explain
Here are a couple of nice photographs of rainbows.
This is one end of a very bright primary rainbow (you
can tell because red is on the outer edge of the bow. Note also
the sky below the rainbow is brighter (whiter) than the sky above the
rainbow. There is just a hint of a supernumerary arc (the faint
bluish green band of light below the violet light on the bottom edge of
the rainbow). (the image is from www.webecoist.com)
The faint secondary
rainbow is clearly visible in this picture. And you can see the
supernumerary arcs on the bottom edge of the primary rainbow. The
bands of light in the arcs get smaller as you move further from the
(the image is from this source
Next we'll look at the formation of mirages. First here's a
drawing showing sunlight striking a tree.
The light is scattered (sent off in all directions by
the tree). You
would see green light coming from the top of the tree is you look back
along Light Ray 1. You'd see brown coming from the tree's trunk
looking along Ray 2.
Here's what the person would see when they look at the tree.
Next imagion there is water on the ground between you and the tree.
1 & 2 from the figure above, they aren't shown in the figure below.
You'd also see rays of light coming from the tree if
you look down at the water. Rays 3 & 4 are being reflected by
the surface of the water.
Now you see the tree when looking up and a reflection of the tree
when looking down toward the ground. The blue light surrounding
the tree (in the reflected image) is light from the sky that is
reflected by the water.
The same effect can be produced by refracted light (below)
Light rays traveling into the warmer lower density air next
to the ground are bent. This is an inferior mirage. The
mirage image is inverted and
below the normal image of the object.
Your brain isn't able to distinquish between these two
situations. Since it's more familiar with light being reflected
by water your brain just assumes that refracted light and a mirage is
thing. The blue light surrounding the inverted image is blue
light coming from the sky.
Here are some examples of inferior mirages.
It looks like water but it's probably not, not in a
dry desert setting like this. (source)
The black road surface gets hotter than the ground on
either side of the road. Light from the sky is being refracted
and sent toward your eyes. An inferior mirage will make a hot
road surface look like it's wet. It looks like light from the sky
is being reflected but it's not. It's being refracted.
Mirages can also form when the ground
Here's what happens if you look at
the top of a mountain.
Now the ground and the air next to the ground are cold. The
light rays are bent as shown above. Ray 1 now hits the ground at
your feet. When you look a little higher in the sky (higher than
you had to look to see Ray 1) you'll now see Ray 2.
This is a superior mirage and will make the
mountain appear taller than it really is.
A superior mirage is a little harder to spot because you only see
one image and the mirage image isn't upside down.
Here are a couple of photographs of superior mirages.
The mirage image is not the nearby boat but the distant cargo
ship. It appears much taller than it really is.
Here tree and buildings on a distant shore line appear taller than
they really are. They've effectively been stretched vertically.
of this image)
Finally I'll try to explain and
illustrate the formation of the green flash. This refers to a
flash or spot of green light that is sometime visible just as the sun
is setting (it is also the name of a brewing company located in
San Diego). It's a little harder to understand.
Here's a very nice photograph (source)
Refraction is involved again in the formation of the green
flash. As the sun sets, rays of white light strike the top of the
atmosphere and are bent. The amount of bending is greatly
Now we've draw three different rays of sunlight striking the
atmosphere at different locations. The person on the ground would
see violet light when looking up at Point C, green light from Point B,
and red light from Point A which is lower in the sky.
If the sun were a point of light in the sky there might be enough
bending that you'd see 6 separate spots of light of different colors
above the horizon as sketched below.
A spot of violet light at Point C a little bit above the horizon
and some red light closer to the horizon at Point C. As the sun
set the points of light would disappear one by one below the horizon.
The sun isn't a point of light, it's a bright disk. So
refraction of sunlight means the sun's disk gets smeared out slightly
into a set of overlapping disks of different colors.
The colors that mix together in the middle produce white light
(not the the dark mix shown above).
And there's one more complication. As the different colors travel
through the atmosphere (and they're taking a long path at sunset when
the sun is low in the sky) the shorter wavelengths get scattered more
than the longer wavelengths. Scattering means the shortest
wavelengths, the blue and violet light, get removed from the beam of
sunlight and don't make it to the ground. So rather than a set of
6 disks of 6 colors you really only have 4 disks as shown below.
And this is what moves below the horizon. If you watch
closely you might just catch the edge of the last disk, the top disk,
disk of green light, before it goes below the horizon.
Because it is the last you'll see just the green light.
A photograph of the real thing is shown below (source)
It's something you might never see. But definitely worth it if