Of the Rainbow

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Of the Rainbow – Edwards talks about the reflexive ability of the rainbow and how we see it.

We shall endeavor to give a full account of the rainbow and such an one as we think if well understood, will be satisfactory to any body, if they are fully satisfied of Sir Isaac Newton’s Different Reflexibility and Refrangibility of the Rays of Light; and if he be not, we refer him to [what] he has said about it, and we are assured if he be a person of an ordinary logacity and anything versed in such matters, by that time he has thoroughly considered it, he’ll be satisfied; and after that let him peruse what we are about to say.

The first question then shall be what is that reflection which we call a rainbow from. I answer from the falling drops of rain, for we never see any rainbow, except it be so that the sun can shine full upon the drops of rain, except the heavens be so clear on one side as to let the uninterrupted rays of the sun come directly upon the rain that [?] falls on the other side. Thus we say it is a sign of fair weather when there is a rainbow in the east, because when there is a rainbow in the east, it is always already fair in the west. For if it be cloudy, there the rays of the sun will be hindered from coming thence to the opposite of drops of rain. It cannot be the cloud from whence this reflection is made, as was once thought, for we almost always see the ends of rainbows come down even in amongst the trees below the hills and to the very ground, where we know there is no part of the cloud there, but what descends in drops of rain; and [I] can convince any man by ocular demonstration in two minutes on a fair day that the reflection is from drops, by only taking a little water in my mouth and standing between the sun and something that looks a little darkish, and spurting of it into the air so as to disperse all into fine drops; and there will appear as complete and plain a rainbow with all the colors as ever was seen in the heavens, and there will appear the same if the sun is near enough to the horizon upon fine drops of water dashed up by a stick from a puddle. The reason why the drops must be fine is because they won’t be thick enough, but here and there a drop, if they are large, and I have frequently heard my countrymen that are used to sawmills say that they have seen a rainbow upon the drops that are dispersed in the air by the violent concussion of the waters in the mill, and what is equivalent to a rainbow. If one take a drop of water upon the end of a stick and hold it up on the side that is opposite to the sun and moving it along towards one side or t’other, you will perceive where the drop is held just as such a distance from the point opposite to the sun that the rays of the sun are much more vividly reflected by it to your eye, than at any other place nearer or further of, and that in the colors of the rainbow too; so that if there had been enough of these drops, there would have appeared a perfect rainbow; and if you have a mind to see more distinctly, you may fill a globular glass bottle with water, the glass of it must be very thin and clear, and it will serve your turn as well as so big a drop of water, and by that means you may also distinctly see that the reflection is from the concave and not from the convex surface.

The next thing that wants a solution is what should cause the reflection to be circular, or which is the same thing what should cause the reflection to be just at such a distance everywhere from the point that is opposite to the sun, and no reflection at all from the drops that are within or without that circle. Why should not all the drops that are within the circle reflect as many rays as those that are in the circle or where the circle is? To resolve this we must consider this one law of reflection and refraction to wit. If the reflecting body be perfectly reflexive, the angle of reflection will be the same as the angle of incidence, but if the body be not perfectly, so the angle will be less than the angle of incidence. By a body perfectly reflexive, I mean one that is so solid as perfectly to resist the stroke of the incident body and not to give way, and does not obstinately resist the stroke of the incident body. So I say that if body a. b. be perfectly reflexive and does not give way at all to the stroke of the incident ray c. d., it will reflect by an angle that shall equal to that by which it fell upon the body a. b. from d. to e (see Figure 1). But if the body a. b. is not able to resist the stroke of the ray c. d. but gives way to it, it will neither be able to reflect by so big an angle but will reflect it. It may be by the line d. f. or d. g., according as the reflexive force of a. b. be greater or lesser. And the bare consideration of this will be enough to convince any man, for we know that there is need of greater force by a great angle than by a little one. If we throw a ball against the floor or wall, it will much easier rebound sideways than right back again, and [if] we throw it sideways against a body that gives way to the stroke of (it may be tried at any time), it will not rebound in so big an angle as if the body were quite hard. So it is the same thing in the body a. b. It might give way so much as to let the ray proceed right on with very little deviation from its old path, and if so, the deviation will be greater and greater in proportion to the resisting power of the body; and if it gives way at all, it will not deviate so much as if it did not at all. Now these drops of water is one of these imperfectly reflexive bodies. If they were perfectly reflexive, we should see those drops that are right opposite to reflect as many rays as those that are just so much on one side, had the liquor but resistance enough to reflect the rays so directly back again. But those rays that fall perpendicularly, or near perpendicularly, upon the concave surface of the drop as from a. to b. (see Figure 2), falling with much greater force than the ray, which falls sideways upon it from e. to b. after the refraction at e., which is made in all pellucid globes. The concave surface has not force enough to stop it and reflect it (what the reflexive force of the concave surface is we are not now disputing), but lets go through and pass right on uninterruptedly. Now the ray h. e. b. and the rays which fall about so obliquely coming with a far lighter stroke the concave surface, has force enough to resist it, and what falls obliquely being far more easily reflexible, reflects it along in the line b. g.; and so in the same manner, the ray c. i. b. will be reflected to k., so that an eye so much sideways as g. or k. will take the rays thus reflected from the drops and no where else; and it being only those ray[s] whose obliquity is adjusted [to] the refractive power that are reflected by it, and they being all reflected out again with such a degree of obliquity, we hence see why the rays be not reflected all ways equally. We hence also see why the rays are only reflected out at the sides of the drop and not directly back again, by that why the eye does not take the rays from any drops but those that are so much sideways of, or on one side of the point that is right opposite to the sun, and so why the parts that are so opposite look dark, and why the parts that are just so much on one side at such a distance all round from the opposite point alone are bright, or which is the same thing why there is such a bright circle.the next grand question is what is it causes the colors of the rainbow, and this question indeed is almost answered already, for it is very evident.