# Why rainbow has a shape of arc and why its ends are bent down.

by paweld
Tags: bent, ends, rainbow, shape
 P: 256 Can anyone explain why rainbow has a shape of arc and why its "ends" are bent down.
 P: 15,319 A rainbow's position is always opposite the sun at a particular angle. If you could see the rainbow in its entirety, you would see that it forms a perfect circle around the point exactly opposite the sun from you. This is a picture of a rainbow as seen from an airplane. Since there's no ground in the way, you can see how the rainbow goes all the way around. Notice the shadow of the airplane where the photographer is taking the pic from. The shadow is dead centre of the rainbow. That's because the sun, the viewer and the centre of the rainbow are all on the same axis.
 P: 2,043 Dont rainbows only occur st specific angles of reflection too? (40 odd degrees rings a bell) You can get double rainbows if there is enough light, on the outer one the colour pattern is reversed (its always much dimmer). I think this is about 50 odd degrees.
P: 488
Why rainbow has a shape of arc and why its ends are bent down.

 Quote by DaveC426913 A rainbow's position is always opposite the sun at a particular angle. If you could see the rainbow in its entirety, you would see that it forms a perfect circle around the point exactly opposite the sun from you. This is a picture of a rainbow as seen from an airplane. Since there's no ground in the way, you can see how the rainbow goes all the way around. Notice the shadow of the airplane where the photographer is taking the pic from. The shadow is dead centre of the rainbow. That's because the sun, the viewer and the centre of the rainbow are all on the same axis.
You can see the rainbow in its entirety by spraying a fine mist with a hosepipe on a sunny day.
Just spray with a circular motion at a point exactly opposite the sun.
ie.with your back towards the sun and a rainbow circle will appear.
The reason why it is arced or circular is because the edge of the arc or circle is the transposition of the edge of the round sun.
P: 488
 Quote by Buckleymanor You can see the rainbow in its entirety by spraying a fine mist with a hosepipe on a sunny day. Just spray with a circular motion at a point exactly opposite the sun. ie.with your back towards the sun and a rainbow circle will appear. The reason why it is arced or circular is because the edge of the arc or circle is the transposition of the edge of the round sun.
So it is not a perfect circle only as perfect as the circle the edge of the sun makes.
PF Gold
P: 1,841
 Quote by Buckleymanor The reason why it is arced or circular is because the edge of the arc or circle is the transposition of the edge of the round sun.
It is nothing to do with the shape of the sun. When sunlight hits a raindrop, some of the light gets reflected through an angle of about 42° (and different colours are reflected through a slightly different angle). For the reflected light to hit your eye, the raindrop needs to be at a position that is 42° away from the direction of your own shadow relative to you. So all of these raindrops lie in a cone of semi-angle 42° with yourself at the vertex.

For more details see Rainbow on Wikipedia.
P: 488
 Quote by DrGreg It is nothing to do with the shape of the sun. When sunlight hits a raindrop, some of the light gets reflected through an angle of about 42° (and different colours are reflected through a slightly different angle). For the reflected light to hit your eye, the raindrop needs to be at a position that is 42° away from the direction of your own shadow relative to you. So all of these raindrops lie in a cone of semi-angle 42° with yourself at the vertex. For more details see Rainbow on Wikipedia.
Well I don't know who wrote the Wiki article but it's wrong.
Take this bit.

Seawater has a higher refractive index than rain water, so the radius of a 'rainbow' in sea spray is smaller than a true rainbow.

The water sprayed from a hosepipe has the same refractive index as rainwater but the radius of the rainbow is smaller than a true rainbow or one cast from sea-spray.
PF Gold
P: 1,841
 Quote by Buckleymanor Well I don't know who wrote the Wiki article but it's wrong. Take this bit. Seawater has a higher refractive index than rain water, so the radius of a 'rainbow' in sea spray is smaller than a true rainbow. The water sprayed from a hosepipe has the same refractive index as rainwater but the radius of the rainbow is smaller than a true rainbow or one cast from sea-spray.
Would you be happier if the article said "subtended angle" instead of "radius"?
P: 488
 Quote by DrGreg Would you be happier if the article said "subtended angle" instead of "radius"?
It would still be wrong if it said subtended angle.
The size of the radius or angle depends more on where the rain, sea spray or hosepipe spray falls from the observer.
The distance from him.
Rather than the refractive index causing the angle.
I suppose you could spray some salt water and some rain water on a sunny day and measure the angles or radia.
The Wiki article does not explain in detail though how that might be it just states the radius is smaller in sea spray.Well depending were you are sat it ain't.
PF Gold
P: 1,841
 Quote by Buckleymanor It would still be wrong if it said subtended angle. The size of the radius or angle depends more on where the rain, sea spray or hosepipe spray falls from the observer. The distance from him. Rather than the refractive index causing the angle. I suppose you could spray some salt water and some rain water on a sunny day and measure the angles or radia. The Wiki article does not explain in detail though how that might be it just states the radius is smaller in sea spray.Well depending were you are sat it ain't.
I don't follow what you are saying here.

You do understand we are talking about the apparent size as seen within the eye (an angle), not a distance in metres?

Light travels in a straight line from the sun, hits a raindrop and gets reflected through about 42° within that raindrop, then then travels in a straight line to your eye. In a salty raindrop the angle is about 0.8° less than in a plain-water raindrop.

There's a nice picture here.
P: 488
 Quote by DrGreg I don't follow what you are saying here. You do understand we are talking about the apparent size as seen within the eye (an angle), not a distance in metres? Light travels in a straight line from the sun, hits a raindrop and gets reflected through about 42° within that raindrop, then then travels in a straight line to your eye. In a salty raindrop the angle is about 0.8° less than in a plain-water raindrop. There's a nice picture here.
I realise that we are talking about the apparent size as seen within the eye the Wiki article was not so clear.
That is why I mentioned spraying salt water and rain water and then measuring the angles.
No need to do that as the picture shows the difference in angles.
Thanks for taking the trouble to find and post.
Would a point source of light instead of the sun form a rainbow or circle in the same way.
P: 15,319
 Quote by Buckleymanor Would a point source of light instead of the sun form a rainbow or circle in the same way.
Yes.
 Sci Advisor PF Gold P: 1,841 The diagrams below illustrate the mechanism. The top-left diagram shows a rainbow in sunlight (or other very distant source). You have to imagine this diagram rotated around the vertical axis to get the circular arc, as shown in the bottom-left diagram. The right-hand diagram shows a rainbow from a closer source of light. Note that the apparent radius (i.e. angle) is larger. If the depth of the rainy area (i.e. distance from back to front relative to the observer) is large, the quality of the rainbow will be degraded. Relative to the observer, the red raindrops are not all in the same direction, unlike the case in sunlight. Instead of seeing all the colours of the rainbow, you are more likely to see a white rainbow with red and blue fringes. The quality will depend on the depth of the rainy area and the distance from the light source. A shallow rainy area will improve the colour (i.e. more rainbow-like) but also decrease the brightness. Attached Thumbnails
P: 488
 The top-left diagram shows a rainbow in sunlight (or other very distant source). You have to imagine this diagram rotated around the vertical axis to get the circular arc, as shown in the bottom-left diagram. The right-hand diagram shows a rainbow from a closer source of light. Note that the apparent radius (i.e. angle) is larger.
So can the distance of the Sun from the Earth's orbit around it have an effect on the size of the cicular arc of a rainbow.
The apparent radius(i.e. angle) being larger in winter and smaller in sumer.
P: 15,319
 Quote by Buckleymanor So can the distance of the Sun from the Earth's orbit around it have an effect on the size of the cicular arc of a rainbow. The apparent radius(i.e. angle) being larger in winter and smaller in sumer.
No. The sun's rays are effectively parallel over the span of a rainbow. Changing the sun's distance will change this by a trivially small angle - minutes or seconds of degrees of arc.

The primary factors in the radius of the arc are the refractive index of water and the geometry of the observer and mist cloud.
 P: 171 Besides water droplets you can also get reflections off ice crystals. Sun dogs and halos are formed that way. On spaceweather yesterday there is a picture of a fogbow at night taken in Northern Canada.. http://spaceweather.com/archive.php?...h=12&year=2009
P: 15,319
 Quote by nucleus Besides water droplets you can also get reflections off ice crystals. Sun dogs and halos are formed that way. On spaceweather yesterday there is a picture of a fogbow at night taken in Northern Canada.. http://spaceweather.com/archive.php?...h=12&year=2009
Note (as you say) that, with ice crystals it's caused by reflection whereas with water it's refraction.

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