equal to AD, and draw CB. For this Line CB shall be the reflected Ray;
the Angle of Reflexion BCP and its Sine BD being equal to the Angle and
Sine of Incidence, as they ought to be by the second Axiom, But if the
refracted Ray be desired, I produce AD to H, so that DH may be to AD as
the Sine of Refraction to the Sine of Incidence, that is, (if the Light
be red) as 3 to 4; and about the Center C and in the Plane ACP with the
Radius CA describing a Circle ABE, I draw a parallel to the
Perpendicular CPQ, the Line HE cutting the Circumference in E, and
joining CE, this Line CE shall be the Line of the refracted Ray. For if
EF be let fall perpendicularly on the Line PQ, this Line EF shall be the
Sine of Refraction of the Ray CE, the Angle of Refraction being ECQ; and
this Sine EF is equal to DH, and consequently in Proportion to the Sine
of Incidence AD as 3 to 4.
In like manner, if there be a Prism of Glass (that is, a Glass bounded
with two Equal and Parallel Triangular ends, and three plain and well
polished Sides, which meet in three Parallel Lines running from the
three Angles of one end to the three Angles of the other end) and if the
Refraction of the Light in passing cross this Prism be desired: Let ACB
[in _Fig._ 2.] represent a Plane cutting this Prism transversly to its
three Parallel lines or edges there where the Light passeth through it,
and let DE be the Ray incident upon the first side of the Prism AC where
the Light goes into the Glass; and by putting the Proportion of the Sine
of Incidence to the Sine of Refraction as 17 to 11 find EF the first
refracted Ray. Then taking this Ray for the Incident Ray upon the second
side of the Glass BC where the Light goes out, find the next refracted
Ray FG by putting the Proportion of the Sine of Incidence to the Sine of
Refraction as 11 to 17. For if the Sine of Incidence out of Air into
Glass be to the Sine of Refraction as 17 to 11, the Sine of Incidence
out of Glass into Air must on the contrary be to the Sine of Refraction
as 11 to 17, by the third Axiom.
[Illustration: FIG. 2.]
Much after the same manner, if ACBD [in _Fig._ 3.] represent a Glass
spherically convex on both sides (usually called a _Lens_, such as is a
Burning-glass, or Spectacle-glass, or an Object-glass of a Telescope)
and it be required to know how Light falling upon it from any lucid
point Q shall be refracted, let QM represent a Ray falling upon any
point M of its first spherical Surface ACB, and by erecting a
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