Uncovering the Mystery of Curving Rainbows: Nature vs. Lab Experiments

[Likith D]

We get a "naturally curved" rainbow in nature
but while trying to mimic a rainbow in lab, we don't see a curved one...
Can't we use the same reason that happens in nature to curve our lab-rainbow

 

[phinds]

We get a "naturally curved" rainbow in nature
but while trying to mimic a rainbow in lab, we don't see a curved one...
Can't we use the same reason that happens in nature to curve our lab-rainbow

If you do a rainbow in the lab it will be curved. I've done a very small rainbow in the yard with a garden hose and of course it was curved. Rainbows are always curved.

If you just shine light through a prism it will not be curved, although I suppose if you had a curved prism the spectrum coming out would be curved. Not sure you could really quite manage that but maybe.

EDIT: and by the way, the rainbow of colors that come out of a prism is not a "rainbow" of the type that forms in the sky even though they are formed for the same reasons.

 

[Buzz Bloom]

Hi Likith:

I have seem a curved rainbow in the spray of hose watering a lawn. Perhaps to see the curved rainbow in a lab requires a somewhat large lab space. I am guessing that the curvature depends on the source of the white light illuminating a spray being near parallel with respect to the entire rainbow created.

Regards,
Buzz

 

[Drakkith]

I am guessing that the curvature depends on the source of the white light illuminating a spray being near parallel with respect to the entire rainbow created.

I believe the radius of curvature of the rainbow depends only on the refractive index of the water droplets. For normal water, the rainbow subtends about 42 degrees from the center to the arc. In other words, if you were to take the arc of the rainbow and continue it around to create a full circle, it would extend across an 84 degree field of view. Forty-two from one side to the 'center' and then another forty-two from the center to the other side. If the droplets were made of seawater or another fluid with a higher refractive index the rainbow would curve more sharply and would extend across a smaller field of view.

 

[A.T.]

I believe the radius of curvature of the rainbow depends only on the refractive index of the water droplets. For normal water, the rainbow subtends about 42 degrees from the center to the arc.

What if the light source isn't the Sun, but a much nearer point source? Still 42 degrees?

 

[Drakkith]

What if the light source isn't the Sun, but a much nearer point source? Still 42 degrees?

Not sure. Someone get a flashlight and a garden hose, stat!

 

[anorlunda]

What if the light source isn't the Sun, but a much nearer point source? Still 42 degrees?

The 42 degrees comes from the spherical geometry of the water droplet. But the appearance of rainbows that we are most familiar with depends on the incoming light rays being parallel. So a distant point source yes. For a close point light source, work out the geometry.

See the recent Insights article. https://www.physicsforums.com/insights/rainbows-not-vampires/

 

[A.T.]

For a close point light source, work out the geometry.

If the illumination isn't approximately parallel, you won't see a rainbow in a volume of water drops.

 

[anorlunda]

If the illumination isn't approximately parallel, you won't see a rainbow in a volume of water drops.

I agree, but you will see reflections from the drops, and maybe even multicolor light. But the shape will be distorted somehow. Look at the figures in the insight article depicting reflection of a single drop. That still applies for nearby point sources. What doesn't apply the same is the relationship between that and neighboring drops.

 

[A.T.]

But the shape will be distorted somehow.

There won't be any distinct shape. If you would move a distant light source closer, the rainbows it creates would just blur out.

 

[leright]

Curved rainbow light is caused by a sequence of refractions between water droplets in air. The reason you see a non-curved rainbow in a prism for instance is because there are only two air-glass interfaces, or two refraction points.

 

[A.T.]

The reason you see a non-curved rainbow in a prism for instance is because there are only two air-glass interfaces, or two refraction points.

It's not about the number of refractions, but more about the shape of the interfaces: spherical vs. planar.

 

[Philip Wood]

A delightful rainbow can be made by sprinkling very small clear plastic beads all over the bottom of a big, empty, open-topped, cubical box. If a compact light source is dangled inside the box, near the central point in the box or somewhat above this point, a rainbow in the shape of a complete circle will be seen if one looks down on the bottom of the box from above the box.

 

[A.T.]

A delightful rainbow can be made by sprinkling very small clear plastic beads all over the bottom of a big, empty, open-topped, cubical box. If a compact light source is dangled inside the box, near the central point in the box or somewhat above this point, a rainbow in the shape of a complete circle will be seen if one looks down on the bottom of the box from above the box.

Good point. If the droplets/beads are distributed over a surface, you can get "rainbows" from a near point light source. But if they are distributed over a volume, you need parallel light rays.

 

[leright]

It's not about the number of refractions, but more about the shape of the interfaces: spherical vs. planar.

Really? I figured a large blob of water in the sky would produce two refractions resulting in straight lines whereas discrete droplets produce the curvature due to a series of refractions. I do agree that the shape of the droplet is also part of it though.

 

[anorlunda]

Really? I figured a large blob of water in the sky would produce two refractions resulting in straight lines whereas discrete droplets produce the curvature due to a series of refractions. I do agree that the shape of the droplet is also part of it though.

 

[A.T.]

figured a large blob of water in the sky would produce two refractions resulting in straight lines

I have no idea why you think a single sphere of water would produce a straight rainbow.

whereas discrete droplets produce the curvature due to a series of refractions.

Each light ray you see as the primary rainbow was refracted twice.

 

[leright]

I'm referring to the arch like shape of the rainbow.

 

[leright]

Thanks guys. I will have to give this more thought.

 

[leright]

Ok. I think I've got it now. I think the key is the paraxial nature of the suns rays since the sun is so far away. The arch is due to the angle the light is refracted, the point of refraction and the distance you are standing from the point of refraction.