116 PHYSICS. 
is formed by the intersection of two contiguous rays in the same 
plane. Fig. 23 exhibits a caustic curve produced by a curved reflecting 
strip. 
c. Refraction of Light.—Dioptrics. 
When a ray of light passes from one medium to another, it experiences a 
change of direction, or becomes broken, i. e. refracted. When the media 
are perfectly homogeneous, the refraction takes place suddenly; as, however, 
in most cases there is a stratification of media, this refraction, strictly 
speaking, takes place in acurve, as has been already referred to in 
Astronomy. This curvature is generally so slight as to be scarcely 
sensible, and but little error is involved by considering refraction to take 
place in straight lines. If, in fig. 24, the horizontal line passing through 7 
separate two different media, as water and air, then the angle formed by 
the incident ray, zw, with the vertical line, mz, is called. the angle of 
incidence. The angle of refraction is that angle formed by the ray, ir, 
after entering the second medium with the same vertical line produced on 
the opposite side. The plane of incidence passes through the incident ray 
and the vertical; the plane of refraction through the same vertical and the 
refracted ray. Generally, the incident ray is refracted into but one line ; 
there are cases, however, in which this ray becomes split into two, as will 
be seen when we come to the subject of polarization. 
For simple or single refraction, to which we here restrict ourselves, the 
following laws present themselves :—Ist. The plane of refraction coincides 
with the plane of incidence. 2d. For the same media, the sine of the angle 
of incidence bears a constant ratio to the sine of the angle of refraction. 
Suppose in pl. 21, fig. 25, / to be a ray of light, incident at the same point 
as, and in the same plane with a vertical, dd’, and there to suffer a 
refraction. If it were desired to determine the angles of incidence and 
refraction on a graduated circle, we may suppose a circle to be described 
about the point of incidence, cutting the two rays. There ad would be 
the sine of the angle of incidence, and cd that of refraction. If the 
angle of incidence were found by direct measurement to be = 15°, then the 
angle of refraction would be 11° 15’; if the former, again, were 60°, the 
latter would be 40° 30’; and the sines of these angles are respectively, 
0.259, 0.194, 0.866, 0.649. Constructing the above proportions we have 
sin. 15° (0.259 sin. 60° 0.866 
sin. 11° 15’ ~ 0.194 — * "4 Sin. 40° 30° — 0.649 #* ‘hat is, the sine 
of the angle of incidence is to the sine of the angle of refraction :: 4:3. 
The index of refraction, four thirds, answers for the case where the ray 
passes from air into water; for other media other indices are required. 
Even in water a change of temperature will produce a different index. 
If the ray pass from water into air, the rays change names, but retain the 
same values; and if m be the index of refraction in the first case, of a ray 
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