Six Lectures on Light | Page 9

wind and
vane, and nothing more. You will immediately understand the meaning
of Bradley's discovery. Imagine yourself in a motionless railway-train,
with a shower of rain descending vertically downwards. The moment
the train begins to move, the rain-drops begin to slant, and the quicker
the motion of the train the greater is the obliquity. In a precisely similar

manner the rays from a star, vertically overhead, are caused to slant by
the motion of the earth through space. Knowing the speed of the train,
and the obliquity of the falling rain, the velocity of the drops may be
calculated; and knowing the speed of the earth in her orbit, and the
obliquity of the rays due to this cause, we can calculate just as easily
the velocity of light. Bradley did this, and the 'aberration of light,' as his
discovery is called, enabled him to assign to it a velocity almost
identical with that deduced by Roemer from a totally different method
of observation. Subsequently Fizeau, and quite recently Cornu,
employing not planetary or stellar distances, but simply the breadth of
the city of Paris, determined the velocity of light: while Foucault--a
man of the rarest mechanical genius--solved the problem without
quitting his private room. Owing to an error in the determination of the
earth's distance from the sun, the velocity assigned to light by both
Roemer and Bradley is too great. With a close approximation to
accuracy it may be regarded as 186,000 miles a second.
By Roemer's discovery, the notion entertained by Descartes, and
espoused by Hooke, that light is propagated instantly through space,
was overthrown. But the establishment of its motion through stellar
space led to speculations regarding its velocity in transparent terrestrial
substances. The 'index of refraction' of a ray passing from air into water
is 4/3. Newton assumed these numbers to mean that the velocity of
light in water being 4, its velocity in air is 3; and he deduced the
phenomena of refraction from this assumption. Huyghens took the
opposite and truer view. According to this great man, the velocity of
light in water being 3, its velocity in air is 4; but both in Newton's time
and ours the same great principle determined, and determines, the
course of light in all cases. In passing from point to point, whatever be
the media in its path, or however it may be refracted or reflected, light
takes the course which occupies least time. Thus in fig. 4, taking its
velocity in air and in water into account, the light reaches G from I
more rapidly by travelling first to O, and there changing its course, than
if it proceeded straight from I to G. This is readily comprehended,
because, in the latter case, it would pursue a greater distance through
the water, which is the more retarding medium.
§ 6. _Descartes' Explanation of the Rainbow_.
Snell's law of refraction is one of the corner-stones of optical science,

and its applications to-day are million-fold. Immediately after its
discovery Descartes applied it to the explanation of the rainbow. A
beam of solar light falling obliquely upon a rain-drop is refracted on
entering the drop. It is in part reflected at the back of the drop, and on
emerging it is again refracted. By these two refractions, and this single
reflection, the light is sent to the eye of an observer facing the drop, and
with his back to the sun.
Conceive a line drawn from the sun, through the back of his head, to
the observer's eye and prolonged beyond it. Conceive a second line
drawn from the shower to the eye, and enclosing an angle of 42½° with
the line drawn from the sun. Along this second line a rain-drop when
struck by a sunbeam will send red light to the eye. Every other drop
similarly situated, that is, every drop at an angular distance of 42½°
from the line through the sun and eye, will do the same. A circular band
of red light is thus formed, which may be regarded as the boundary of
the base of a cone, with its apex at the observer's eye. Because of the
magnitude of the sun, the angular width of this red band will be half a
degree.
From the eye of the observer conceive another line to be drawn,
enclosing an angle, not of 42½°, but of 40½°, with the prolongation of
the line drawn from the sun. Along this other line a rain-drop, at its
remote end, when struck by a solar beam, will send violet light to the
eye. All drops at the same angular distance will do the same, and we
shall therefore obtain a band of violet light of the same width as the red
band. These two bands constitute the limiting colours of