Lenses and Waves

138 CHAPTER 4
refraction. 112 For reflection, he
considered BD – a line of light in the
most realist sense of the word –
colliding obliquely with a reflecting
surface EF (Figure 42). He argued
that, after B hits the surface, this end
of the line of light rebounds while end
D continues its way, resulting in the
rotation of BD around its center Z.
This rotation lasts until D hits the
surface and the line of light is in position . The line of light then continues
towards . From the symmetry of the situation the equivalence of the
angles of incidence and reflection follows directly.
To substantiate his claim, Barrow invoked a general ‘law’ of motion:
“… that it is constantly found in nature, when a straight movement degenerates into a
circular one, that it is the extreme parts of the moving objects that direct and control all
motion.” 113
He applied the same law to derive
the sine law (Figure 43). On
entering the more resisting
medium below EF, point B of the
line of light BD will be slowed
down while D continues with the
original speed. As a consequence
DB will be rotated around a point
Z until D also reaches the ‘denser’
medium. Then the line of light
will continue along a straight path.
Now, the proportion between ZD
and ZB is constant for any angle
of incidence and depends upon
the particular difference of the
densities. From this it easily
follows that for i =GBM and
r =N, sin i : sin r = ZD : ZB. 114 After thus explaining refraction into a rarer
medium and total reflection, Barrow was ready to elaborate the ‘Optic
Science’ of his lectures in the common manner:
“…considering rays as one-dimensional (seeing that the other dimensions, in which
physicists delight, have no importance for the calculations here undertaken).” 115
Figure 42 Barrow’s explanation of reflection.
Figure 43 Explanation of refraction.
112 Like Maignan in his Perspectiva Horaria (1648), Barrow added a derivation of the law of reflection which
Hobbes had not provided. See Shapiro, “Kinematic optics”, 175-178.
113 Barrow, Lectiones, [28].
114 Barrow, Lectiones, [29-31]
115 Barrow, Lectiones, [39-41]