Opticks

by Isaac Newton

And hence I gather, that the Light which makes the Fringes upon the Paper is not the same Light at all distances of the Paper from the Knives, but when the Paper is held near the Knives, the Fringes are made by Light which passes by the edges of the Knives at a less distance, and is more bent than when the Paper is held at a greater distance from the Knives.

Fig. 3.

Obs. 10. When the Fringes of the Shadows of the Knives fell perpendicularly upon a Paper at a great distance from the Knives, they were in the form of Hyperbola's, and their Dimensions were as follows. Let CA, CB [in Fig. 3.] represent Lines drawn upon the Paper parallel to the edges of the Knives, and between which all the Light would fall, if it passed between the edges of the Knives without inflexion; DE a Right Line drawn through C making the Angles ACD, BCE, equal to one another, and terminating all the Light which falls upon the Paper from the point where the edges of the Knives meet; eis, fkt, and glv, three hyperbolical Lines representing the Terminus of the Shadow of one of the Knives, the dark Line between the first and second Fringes of that Shadow, and the dark Line between the second and third Fringes of the same Shadow; xip, ykq, and zlr, three other hyperbolical Lines representing the Terminus of the Shadow of the other Knife, the dark Line between the first and second Fringes of that Shadow, and the dark line between the second and third Fringes of the same Shadow. And conceive that these three Hyperbola's are like and equal to the former three, and cross them in the points i, k, and l, and that the Shadows of the Knives are terminated and distinguish'd from the first luminous Fringes by the lines eis and xip, until the meeting and crossing of the Fringes, and then those lines cross the Fringes in the form of dark lines, terminating the first luminous Fringes within side, and distinguishing them from another Light which begins to appear at i, and illuminates all the triangular space ipDEs comprehended by these dark lines, and the right line DE. Of these Hyperbola's one Asymptote is the line DE, and their other Asymptotes are parallel to the lines CA and CB. Let rv represent a line drawn any where upon the Paper parallel to the Asymptote DE, and let this line cross the right lines AC in m, and BC in n, and the six dark hyperbolical lines in p, q, r; s, t, v; and by measuring the distances ps, qt, rv, and thence collecting the lengths of the Ordinates np, nq, nr or ms, mt, mv, and doing this at several distances of the line rv from the Asymptote DD, you may find as many points of these Hyperbola's as you please, and thereby know that these curve lines are Hyperbola's differing little from the conical Hyperbola. And by measuring the lines Ci, Ck, Cl, you may find other points of these Curves.

For instance; when the Knives were distant from the hole in the Window ten Feet, and the Paper from the Knives nine Feet, and the Angle contained by the edges of the Knives to which the Angle ACB is equal, was subtended by a Chord which was to the Radius as 1 to 32, and the distance of the line rv from the Asymptote DE was half an Inch: I measured the lines ps, qt, rv, and found them 0'35, 0'65, 0'98 Inches respectively; and by adding to their halfs the line 1/2 mn, (which here was the 128th part of an Inch, or 0'0078 Inches,) the Sums np, nq, nr, were 0'1828, 0'3328, 0'4978 Inches. I measured also the distances of the brightest parts of the Fringes which run between pq and st, qr and tv, and next beyond r and v, and found them 0'5, 0'8, and 1'17 Inches.

Obs. 11. The Sun shining into my darken'd Room through a small round hole made in a Plate of Lead with a slender Pin, as above; I placed at the hole a Prism to refract the Light, and form on the opposite Wall the Spectrum of Colours, described in the third Experiment of the first Book. And then I found that the Shadows of all Bodies held in the colour'd Light between the Prism and the Wall, were border'd with Fringes of the Colour of that Light in which they were held. In the full red Light they were totally red without any sensible blue or violet, and in the deep blue Light they were totally blue without any sensible red or yellow; and so in the green Light they were totally green, excepting a little yellow and blue, which were mixed in the green Light of the Prism. And comparing the Fringes made in the several colour'd Lights, I found that those made in the red Light were largest, those made in the violet were least, and those made in the green were of a middle bigness. For the Fringes with which the Shadow of a Man's Hair were bordered, being measured cross the Shadow at the distance of six Inches from the Hair, the distance between the middle and most luminous part of the first or innermost Fringe on one side of the Shadow, and that of the like Fringe on the other side of the Shadow, was in the full red Light 1/37-1/4 of an Inch, and in the full violet 7/46. And the like distance between the middle and most luminous parts of the second Fringes on either side the Shadow was in the full red Light 1/22, and in the violet 1/27 of an Inch. And these distances of the Fringes held the same proportion at all distances from the Hair without any sensible variation.

So then the Rays which made these Fringes in the red Light passed by the Hair at a greater distance than those did which made the like Fringes in the violet; and therefore the Hair in causing these Fringes acted alike upon the red Light or least refrangible Rays at a greater distance, and upon the violet or most refrangible Rays at a less distance, and by those actions disposed the red Light into Larger Fringes, and the violet into smaller, and the Lights of intermediate Colours into Fringes of intermediate bignesses without changing the Colour of any sort of Light.

When therefore the Hair in the first and second of these Observations was held in the white beam of the Sun's Light, and cast a Shadow which was border'd with three Fringes of coloured Light, those Colours arose not from any new modifications impress'd upon the Rays of Light by the Hair, but only from the various inflexions whereby the several Sorts of Rays were separated from one another, which before separation, by the mixture of all their Colours, composed the white beam of the Sun's Light, but whenever separated compose Lights of the several Colours which they are originally disposed to exhibit. In this 11th Observation, where the Colours are separated before the Light passes by the Hair, the least refrangible Rays, which when separated from the rest make red, were inflected at a greater distance from the Hair, so as to make three red Fringes at a greater distance from the middle of the Shadow of the Hair; and the most refrangible Rays which when separated make violet, were inflected at a less distance from the Hair, so as to make three violet Fringes at a less distance from the middle of the Shadow of the Hair. And other Rays of intermediate degrees of Refrangibility were inflected at intermediate distances from the Hair, so as to make Fringes of intermediate Colours at intermediate distances from the middle of the Shadow of the Hair. And in the second Observation, where all the Colours are mix'd in the white Light which passes by the Hair, these Colours are separated by the various inflexions of the Rays, and the Fringes which they make appear all together, and the innermost Fringes being contiguous make one broad Fringe composed of all the Colours in due order, the violet lying on the inside of the Fringe next the Shadow, the red on the outside farthest from the Shadow, and the blue, green, and yellow, in the middle. And, in like manner, the middlemost Fringes of all the Colours lying in order, and being contiguous, make another broad Fringe composed of all the Colours; and the outmost Fringes of all the Colours lying in order, and being contiguous, make a third broad Fringe composed of all the Colours. These are the three Fringes of colour'd Light with which the Shadows of all Bodies are border'd in the second Observation.

When I made the foregoing Observations, I design'd to repeat most of them with more care and exactness, and to make some new ones for determining the manner how the Rays of Light are bent in their passage by Bodies, for making the Fringes of Colours with the dark lines between them. But I was then interrupted, and cannot now think of taking these things into farther Consideration. And since I have not finish'd this part of my Design, I shall conclude with proposing only some Queries, in order to a farther search to be made by others.