Rainbows can be full circles. However, the average observer sees only an
arc formed by illuminated droplets above the ground, and centred on a line
from the sun to the observer's eye. In a primary rainbow, the arc shows
red on the outer part and violet on the inner side. This rainbow is caused
by light being refracted when entering a droplet of water, then reflected
inside on the back of the droplet and refracted again when leaving it. In
a double rainbow, a second arc is seen outside the primary arc, and has
the order of its colours reversed, with red on the inner side of the arc.
A rainbow is not located at a specific distance from the observer, but
comes from an optical illusion caused by any water droplets viewed from a
certain angle relative to a light source. Thus, a rainbow is not an object
and cannot be physically approached. Indeed, it is impossible for an
observer to see a rainbow from water droplets at any angle other than the
customary one of 42 degrees from the direction opposite the light source.
Even if an observer sees another observer who seems "under" or "at the end
of" a rainbow, the second observer will see a different rainbow—farther
off—at the same angle as seen by the first observer.
Rainbows span a continuous spectrum of colours. Any distinct bands
perceived are an artefact of human colour vision, and no banding of any
type is seen in a black-and-white photo of a rainbow, only a smooth
gradation of intensity to a maximum, then fading towards the other side.
For colours seen by the human eye, the most commonly cited and remembered
sequence is Newton's sevenfold red, orange, yellow, green, blue, indigo
and violet,remembered by the mnemonic, Richard Of York Gave Battle In Vain
Rainbows can be caused by many forms of airborne water. These include not
only rain, but also mist, spray, and airborne dew.A rainbow is not located
at a specific distance from the observer, but comes from an optical
illusion caused by any water droplets viewed from a certain angle relative
to a light source. Thus, a rainbow is not an object and cannot be
physically approached. Indeed, it is impossible for an observer to see a
rainbow from water droplets at any angle other than the customary one of
42 degrees from the direction opposite the light source.
Even if an observer sees another observer who seems "under" or "at the end
of" a rainbow, the second observer will see a different rainbow—farther
off—at the same angle as seen by the first observer. Rainbows span a
continuous spectrum of colours. Any distinct bands perceived are an
artefact of human colour vision, and no banding of any type is seen in a
black-and-white photo of a rainbow, only a smooth gradation of intensity
to a maximum, then fading towards the other side. Rainbows can be
caused by many forms of airborne water. These include not only rain, but
also mist, spray, and airborne dew. source: Wikpedia
Q1: What is a rainbow?
A1: Observationally, the rainbow is a circular arc of several colours seen
in rain or spray opposite the sun and centered around the shadow of your
head. The rainbow’s colours are in concentric bands, and while they vary
slightly from one bow to the next, the colours are always arranged in
spectral order: red, orange, yellow, green, blue, and violet. While you
are unlikely to see all of these colours in a given rainbow, their order
does not change. For the inner (or primary) rainbow, red is on the
outside; for the outer (or secondary) rainbow, red is on the inside.
Optically, the rainbow is just a distorted image of the sun. Raindrops
perform this rearranging of sunlight via reflection and refraction. Think
of the drops as imperfect one-way mirrors: most light passes through them,
but that forming the rainbow is reflected from their rear surfaces. In
addition, as sunlight passes from air to water (or vice versa) it
is deviated from its original path, with blue light being deviated more
than red. As indicates, this combination of refraction and reflection
occurs at each air-water boundary. However, the light forming the primary
rainbow is that refracted on entering the drop, reflected at its rear and
refracted a second time on exiting.
Q2: When and where can I expect to see a
A2: You can see the rainbow whenever you look opposite the sun at sunlit
raindrops (or spray drops). The rainbow occurs because raindrops do not
scatter sunlight uniformly in all directions . Consider a ray passing
through the middle of the drop. It is deviated by 180°, returning in the
direction that it entered (ray Q in is closest to this ray). As rays
strike the drop at ever more glancing angles, the combined refractions and
reflection bend the rays through smaller and smaller angles. This does not
continue indefinitely. One ray in particular is bent by 138°, the minimum
deviation (ray M). Rays that enter the drop more obliquely are deviated by
more than 138°. In contrast to other rays, this minimum
deviation ray has a great many neighbors leaving the drop at nearly
the same angle. It is this concentration of light 138° from the sun that
forms the primary rainbow.
We translate the rainbow’s geometry to a more convenient reference point,
the shadow of your head. Whenever you are illuminated by sunlight, the
shadow of your head is 180° from the sun. The shadow of your head thus
covers the antisolar point, the point directly opposite the sun.
So the primary bow is a 42°-radius circle (180°-138° = 42°) centered on
the antisolar point. All rays other than the minimum deviation ray simply
add to the general brightness within this 42°-radius circle. Thus the sky
within the primary rainbow may look bright compared to the brightness of
the surrounding sky. By the same logic, the sky outside an intense
secondary rainbow will be relatively bright. The reason is that rays
exceeding the secondary rainbow’s minimum deviation are seen here (see A5
below). A natural corollary of this enhanced primary and secondary
brightness is that the sky between bright rainbows looks dark (see A12
Q3: What causes the rainbow’s circular
A3: Many drops acting in concert cause the rainbow, and all of these must
be at the same angle from the sun (i.e., the same angle from the
antisolar point). Thus at any instant, only those drops before you that
are on a 42° circle centered about the antisolar point can send you the
concentrated rainbow light. These drops may be at any distance, but must
be on the 42° circle. Put another way, the rainbow is a mosaic of light
sent to you by many raindrops as they fall through the surface of the
imaginary cone whose tip is at your eye and whose radius is 42° .
Q4: What causes the rainbow’s colours?
A4: The rainbow’s colours arise because the minimum deviation ray occurs
at a slightly different angle for each colour. A prism’s refraction of
white light into a spectrum is similar to the rainbow’s colour separation.
Because blue light at minimum deviation is bent through a greater angle
than red light, the red light is closer to the sun. As a consequence, red
will be on the outside of the primary bow, closest to the sun, and blue
will be toward the inside. Although an indefinite number of colours is
possible, their sequence across the bow is not arbitrary. From the outside
to the inside of the primary this spectral sequence is: red, orange,
yellow, green, blue, violet.
A single fact explains the opposite colour orders of the secondary and
primary rainbows: red light at minimum deviation is bent less than blue
light, and thus red appears closer to the sun. However, because minimum
deviation rays for the secondary are bent through more than 180° (see A5 )
“closer to the sun” now means that red appears on the secondary rainbow’s
inner edge. In essence, deviating sunlight through more than 180° turns
the rainbow colours inside out.
Q5: What causes double rainbows?
A5: The path of a light ray (ray M) that contributes to the outer (or
secondary) rainbow. This ray is reflected twice within the drop.
Because each internal reflection is paired with a refraction of light out
of the drop, less light is available to form the secondary bow, and thus
it is less intense than the primary. At minimum deviation, this
secondary-rainbow light is bent through an angle of about 231°, which
places the secondary rainbow 51° from the antisolar point (51°= 231°-180.
Because the secondary rainbow is inherently dimmer than the primary, it
may not always be visible. However, if the primary rainbow is very bright,
look for its fainter secondary companion 9° outside it .
Q6: Why are rainbows often incomplete?
A6: Since the raindrops are falling, their supply must be uninterrupted if
the bow is to last. Because the edge of a rain shaft can pass quickly
across the position where the rainbow might occur, the bow can appear or
disappear rapidly. As long as you see sunlit drops at the minimum
deviation (or rainbow) angle, the bow will be with you. However, if any
part of the circle where the rainbow can occur is devoid of either drops
or direct sunlight, then that part of the bow will not form, which
accounts for the partial bows we often see . Because the rainbow’s angular
size and angular distance from the sun are fixed, we cannot see a rainbow
in a distant shower if the sun is higher than 42° above the horizon
(assuming that we are on level ground).
Q7: Can I ever see an entire rainbow circle?
A7: Yes, anytime that you can see many sunlit drops in all directions from
the antisolar point, the rainbow circle will be complete. For example, you
could see the rainbow circle from atop a mountain, high hill or building,
or an airplane in flight. Less ambitiously, you can see the complete
circle if you fill the air before you with sunlit spray that extends 42°
from the antisolar point. Note that while this spray bow looks
smaller than one seen in a distant shower, its angular size is the
Q8: How big is the rainbow?
A8: The primary rainbow’s angular radius is about 42° and its width is
about 2°. The secondary’s angular radius is about 51° and its width is
about 3°. Neither bow is an object, so neither has a linear size.
However, we typically use our perception of an object’s angular size and
our estimate of its distance from us to infer its linear size.
Experience and expectation combine to make these inferences fairly
accurate for familiar objects. The rainbow has a fixed angular size and we
plausibly (but erroneously) equate its distance with that of the rain or
spray in which we see the bow. Everyday experience tells us that, for a
fixed angular size, objects that appear more distant are larger
than those nearby. Despite the fact that the rainbow is not an object, we
mistakenly assume that our usual rules relating angular and linear size
apply. Thus rainbows seen in a distant shower are compellingly large,
while those in a nearby spray seem small. Yet neither bow has a linear
size, just a fixed angular size.
Q9: How many colours does a rainbow have?
A9: Quite literally, as many as you think you see, whether that number is
three or 300! For good perceptual reasons, we recognize discrete
bands of colour in the rainbow . However, the number of rainbow colours is
actually indeterminate, with each colour blending smoothly into the next
Q10: Why is the sky inside the primary rainbow
A10: See A2 above.
Q11: Why are bright rainbows most vivid near
A11: Large raindrops flatten as they fall but smaller ones do not. As a
result, all sizes of raindrops contribute to the rainbow near its base,
and large drops make this part of the bow both bright and colourful.
However, as we approach the top of the arch only small drops contribute to
the rainbow, and these yield a less intense, more pastel bow.
Q12: Why is the sky dark between the
primary and secondary rainbows?
A12: By definition, raindrops between the bows cannot send you any light
that contributes to either the primary or secondary. In other words, light
that has been internally reflected once (the primary) or twice (the
secondary) by water drops does not reach you from this part of the sky, so
the sky looks comparatively dark there. This dark band is known as Alexander’s
dark band (Chapter 4) and is most evident if the primary and
secondary bows are bright .
Q13: Why and when do red or orange rainbows
A13: Near sunrise and sunset, scattering of sunlight over very long paths
through the atmosphere can make direct sunlight noticeably reddish or
orangish. Since direct sunlight shining on water drops causes the rainbow,
the resulting rainbows will have a pronounced red or orange cast (see
Greenler 1980, Plate 1-7; Minnaert 1993, Plates 11-12).
Q14: What is a cloudbow, and when can I expect
to see one?
A14: A cloudbow is a water-drop bow caused by the same optics that
generates the rainbow. However, cloud droplets are about 10 to 100 times
smaller than raindrops or spray drops. An interference theory of the
rainbow explains (1) the nearly colourless appearance of bows formed by
these small drops, (2) the supernumerary bows that accompany both
cloudbows and rainbows . A cloudbow may be visible when you fly above a
deck of stratus clouds and can see your airplane’s shadow on them.
Alternatively (and more arduously), you can see a cloudbow if you climb
above a sunlit fog bank (i.e., stratus near the ground) that
envelops the base of a hill or mountain. There you look for the cloudbow
about 40° from the shadow of your head.
Q15: Can I ever see rainbows on the ground?
A15: Yes, if the ground is covered with sunlit dew, you may see the
colourful dewbow. Like the rainbow, the dewbow’s light comes from a
circular set of directions that are 42° from the antisolar point. However,
because we know that dew lies on the ground before us, we have the
compelling sense that the dewbow is a hyperbola (or an ellipse if the sun
is high in the sky). (See Greenler 1980, p. 17, Plate 1-12 and Minnaert
1993, pp. 202-203.)
Q16: What is a lunar rainbow and why is it white?
A16: Like the sun, the moon can also generate rainbows. However, because
moonlight is much less intense than sunlight, the lunar rainbow usually is
too dim for us to see any colours in it. Recall that even under a full
moon, objects that look vividly coloured during the day appear only in
shades of gray. Thus the lunar rainbow is white Minnaert 1993, pp.
Q17: What are the pale green and purple
arcs sometimes seen within the primary rainbow?
A17: These are the supernumerary rainbows. Despite their
superfluous-sounding name, they are an integral part of the rainbow . In
fact, explaining how supernumeraries occur also explains the primary and
secondary rainbows (see A14 above).
Q18: Why does a rainbow grow brighter
and darker so quickly?
A18: See A6 above.
Q19: Can I touch the rainbow or reach its end?
A19: No. Because the rainbow is an image, not an object, you can
never reach or touch it . However, in the same way that you can touch a
mirror but not your image in it, you can touch the water drops
that generate the bow. For example, if you make a rainbow in a sprinkler’s
sunlit spray, you can certainly touch the spray. That is quite different
from the impossible feat of touching the rainbow image.
About Colour Terminology
Given colour theory’s long and fractious history, it is not surprising
that many different systems have arisen for describing colour. The table
below lists several common colour schemes and their roughly equivalent
terms. Entries in any given column may not be identical because the
various systems themselves are not completely compatible. To further
complicate matters, many other independent (although highly structured)
colour-naming systems are used in commerce and industry. For thorough
reviews of colour terminology, see Billmeyer and Saltzman (1981) and
Zwimpfer’s beautifully illustrated chapter “Colour designation and
vividness or purity
saturation or tint
tone or lightness
Bibliography -- Appendix
Billmeyer, Fred W., Jr., and Max Saltzman, 1981: Principles of Colour
Technology (John Wiley and Sons, New York, 240 pp.; 2nd edition).
Chevreul, Michel-Eugene, 1987: The Principles of Harmony and Contrast
of Colours and Their Applications to the Arts, Faber Birren, ed.
(Schiffer Publishing Ltd., West Chester, PA, 191 pp.; based on the English
translation published by Henry G. Bohn (London, 1854)).
Greenler, Robert, 1980: Rainbows, Halos, and Glories (Cambridge
University Press, Cambridge, UK, 195 pp.).
Herbert, Robert L., 1991: Georges Seurat, 1859-1891 (Metropolitan
Museum of Art, New York, 450 pp.).
Minnaert, Marcel G. J., 1993: Light and Colour in the Outdoors
(Springer-Verlag, New York, 417 pp.; English translation by Len Seymour).
Zwimpfer, Moritz, 1988: Colour, Light, Sight, Sense (Schiffer
Publishing Ltd., West Chester, PA, n. p.).
Notes and References -- Appendix
Your hands and arms provide a built-in angular measure. Extend your arm
straight and splay out the fingers on that hand, keeping your palm
outward. The angular distance between the tips of your outstretched thumb
and little finger is about 22°, so two hand spans cover 44°, slightly more
than the primary rainbow’s radius. Thus if you put your thumb over your
head’s shadow and measure a distance of two outstretched hand spans from
it, you will be looking at the primary rainbow’s position. .
A pigment mixture’s tone increases as black is added to it (i.e.,
lightness and tone change in opposite senses). Confusingly, “tint” is now
sometimes a synonym for “hue.” (Chevreul 1987, p. 70 (paragraph 148);
Herbert 1991, p. 381) .
The Munsell System is a large collection of colour samples each of which
differs from its immediate neighbor by a fixed perceptual interval of hue,
chroma, or value. With its carefully measured colour samples, this
practical and fairly rigorous system has long had many commercial
applications. (Billmeyer and Saltzman 1981, pp. 28-30)