arc DQ, which will represent a wave emanating from the point F.
Then the wave TG, after having passed through the glass, must form the
wave QD; and for this I observe that the time taken by the light along
GD in the glass must be equal to that taken along the three, TA, AB,
and BQ, of which AB alone is within the glass. Or rather, having taken
AS equal to 2/3 of AT, I observe that 3/2 of GD ought to be equal to
3/2 of SB, plus BQ; and, deducting both of them from FD or FQ, that FD
less 3/2 of GD ought to be equal to FB less 3/2 of SB. And this last
difference is a given length: and all that is required is to draw the
straight line FD from the given point F to meet VG so that it may be
thus. Which is a problem quite similar to that which served for the
first of these constructions, where FD plus 3/2 of GD had to be equal
to a given length.
In the demonstration it is to be observed that, since the arc BC falls
within the glass, there must be conceived an arc RX, concentric with
it and on the other side of QD. Then after it shall have been shown
that the piece G of the wave GT arrives at D at the same time that the
piece T arrives at Q, which is easily deduced from the construction,
it will be evident as a consequence that the partial wave generated at
the point D will touch the arc RX at the moment when the piece Q shall
have come to R, and that thus this arc will at the same moment be the
termination of the movement that comes from the wave TG; whence all
the rest may be concluded.
Having shown the method of finding these curved lines which serve for
the perfect concurrence of the rays, there remains to be explained a
notable thing touching the uncoordinated refraction of spherical,
plane, and other surfaces: an effect which if ignored might cause some
doubt concerning what we have several times said, that rays of light
are straight lines which intersect at right angles the waves which
travel along them.
[Illustration]
For in the case of rays which, for example, fall parallel upon a
spherical surface AFE, intersecting one another, after refraction, at
different points, as this figure represents; what can the waves of
light be, in this transparent body, which are cut at right angles by
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