Isaac Newton Page 8-9

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a lot of when the celebrity manner, if ACBD (in

Fig. three ] reprefent a Glafs ſpherically gibbous on each each (uſually referred to as a Lens, ſuch as could be a could be a, or Spectacle glaſs, or AN Object glaſs of a Teleſcope) and or not it's needed to understand however lightweight falling upon it from any lucid purpose Q

ſhall be refracted, let Q M repreſent a Ray

falling upon any purpose M of its firſt ſpherical

Surface ACB, and by building a Perpendicular

to the Glaſs at the purpose M, notice the firſt re-

fracted Ray M N by the Proportion of the

Sines seventeen to eleven.

Let that Ray in going out of the Glaſs be incident upon N, and so notice

the ſecond refracted Ray weight unit by the Proporti-

on of the Sines eleven to seventeen.

And when the ſame manner might the Refraction be found once the

Lens is gibbous on one ſide and Plane or Con-

cave on the opposite, or bowl-shaped on each each.

A X. VI.

Homogeneal Rays that ensue feveral

Points of any Object, and fall sheer or almoſt sheer on any reflective or refract- ing Plane or ſpherical Surface, ſhall afterward diverge from ſo several alternative Points, or be Parallel to ſo several alternative Lines, or converge to ſo several alternative Points, either accurately or with none with none.

and therefore the and therefore the can happen, if the

Rays be mirrored or refracted ſucceſſively by 2 or 3 or additional Plane or Spherical Surfaces.

the purpose from that Rays diverge or to

which they converge could also be referred to as their Focus.

and therefore the focus of the incident Rays being gi-

ven, that of the mirrored or refracted ones might

be

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   be found by finding the Refraction of any two Rays, as above; or more readily thus.

   

  Caf. 1. Let ACB [in Fig. 4.] be a reflecting or

refracting Plane, and the focus of the incident Rays, and Q q C a perpendicular to that Plane.

   And if this perpendicular be produced to 9,

ſo that q C be equal to QC, the point q, fhall

be the focus of the reflected Rays. 

   Or if qC be taken on the ſame ſide of the Plane with QC and in Proportion to a C as the Sine of Incidence to the Sine of Refraction, the point q ſhall be the Focus of the refracted Rays.

   

    Caf.2. Let ACB [in Fig. 5.] be the reflecting

Surface of any Sphere whoſe Center is E. Bi-

ſect any Radius thereof (fuppofe EC) in T,

and if in that Radius on the ſame fide the point T you take the Points Q and q, ſo that TO, TÉ, and T , be continual Proportionals, and the point Q be the focus of the incident Rays, the point q ihall be the Focus of the reflected ones.

 Cal 3. Let ACB [in Fig. 6.] be the refracting

Surface of any Sphere whole Center is E. In

any Radius thereof E C produced both ways

take ET and Ct equal to one another and fe-

verally in ſuch Proportion to that Radius as

the leffer of the Sines of Incidence and Re-

fraction hath to the difference of thoſe Sines.

 

  And then if in the ſame Line you find any two Points Q and q, ſo that TQ be to ET as Et

to t q, taking t q the contrary way from t which TQ lieth from T, and if the Point Q be the Focus of any incident Rays, the Point q ſhall be the Focus of the refracted ones.

                And

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