Lenses and Waves

116 CHAPTER 4
things moved naturally in a straight line through some substance that will
receive them, passage along the perpendicular to the surface of the body in
which passage takes place is the easiest.” 36 A couple of lines further, Alhacen
continued: “Therefore, the motion [of the light] will be deviated toward a
direction in which it is more easily moved than in its original direction. But
the easier motion is along the perpendicular, and that motion which is closer
to the perpendicular is easier than the more remote.” 37 In the case of
refraction away from the normal Alhacen abandoned the appeal to the
easiest path. He considered the components of the ‘motion’ again and stated
without argument that the parallel component is increased. Besides being
inconsistent, Alhacen’s account of refraction remained qualitative, as he did
not attempt to determine to what degree a refraction ray was bent towards
the normal, nor to what proportion the parallel component was altered.
Alhacen’s account of refraction primarily consists of an experimental
analysis. In Risner’s edition it covers the first eleven or twelve propositions
of the seventh book, which return in the second chapter of Witelo’s part. In
the tenth chapter the latter added to the quantitative account of refraction by
providing a table – supposedly observational – of angles of refraction for a
set of incident rays.
In Alhacen’s accounts of reflection and refraction two levels of inference
can be distinguished. In the first place, the analysis of rays in their
perpendicular and parallel components revealed some deeper lying
mathematical structure of both phenomena. It unified his accounts to some
extent, although he did not assume the parallel component unaltered in all
cases like Descartes would later do. The second level involves mechanical
analogies that illuminate rather than prove the mathematical analyses of
reflected and refracted rays. The causal account provided additional support
for the properties of reflection and refraction, but the ultimate justification
was empirical. 38 In this regard the analogies can be considered to serve
didactical purposes.
Alhacen’s analogies do not - and were not intended to - explain refraction
and reflection by deriving their properties from an account of the nature of
light. That is the way Huygens and his fellow seventeenth-century students
of optics understood ‘explaining the properties of light’ and which his waves
of light would have to bring about. Whereas the rectilinearity of rays
followed rather naturally from Alhacen’s understanding of forms, reflection
and refraction are discussed in terms of light rays instead of interactions
between forms with reflecting and refracting substances. The ideals of
36 Risner, Optica thesaurus, 241. “Omnium autem moterum naturaliter, que recte moventur per aliquod
corpus passibile, transitus super perpendicularem, que est in superficie corperis in quo est transitus, erit
facilior.” Translation: Lindberg, “Cause”, 26.
37 Risner, Optica thesaurus, 241. “...: accidit ergo, ut declinetur ad partem motus, in quam facilius movebitur,
quàm in partem, in quam movebatur : sed facilior motuum est super perpendicularem: & quod vicinius est
perpendiculari, est facilius remotiore.” Translation (amended): Lindberg, “Cause”, 27.
38 Alhacen, Optics I, lxi (Sabra’s introduction); Risner, Optica thesaurus, XVII-XIX (Lindberg’s introduction).