Hero of Alexandria, in his *Catoptrics* (first century BC),
also maintained
that light travels with infinite speed. His argument was by analogy with
the free fall of objects. If we throw an object horizontally with a
relatively small velocity then it manifestly does not move in a
straight-line. However, if we throw an object horizontally with a
relatively large velocity then it appears to move in
a straight-line to begin with, but eventually deviates from this
path. The larger the velocity with which the object is thrown, the longer
the initial period of apparent rectilinear motion. Hero reasoned that
if
an object were thrown with an infinite velocity then it would move in
a straight-line forever. Thus, light, which travels in a straight-line,
must move with an infinite velocity. The erroneous idea that light
travels with
an *infinite*
velocity persisted until 1676, when
the
Danish astronomer Olaf Römer demonstrated that light must have a
*finite*
velocity, using his timings
of the successive eclipses of the satellites of Jupiter, as they passed
into the
shadow of the planet.

The first person to realize that light actually travels from the object seen to the eye was the Arab philosopher ``Alhazan'' (whose real name was Abu'ali al-hasan ibn al-haytham), who published a book on optics in about 1000 AD.

The law of *reflection* was correctly formulated in Euclid's book.
Hero of Alexandria demonstrated that, by adopting the rule that light
rays
always travel between two points by the *shortest path* (or, more
rigorously,
the extremal path), it is possible to derive the law of reflection
using geometry.

The law of *refraction* was studied experimentally by Claudius Ptolemy
(100-170AD), and is reported in Book V of his *Catoptrics*.
Ptolemy formulated a very inaccurate
version of
the law of refraction, which only works when the light rays are almost
normally
incident on the interface in question. Despite its obvious inaccuracy,
Ptolemy's
theory of refraction persisted for nearly 1500 years.
The true law of refraction was discovered empirically by the Dutch
mathematician Willebrord Snell in 1621. However, the French philosopher
René Descartes was the first to publish, in his
*La Dioptrique* (1637), the now familiar
formulation of the law of refraction in terms of sines. Although there was much controversy at
the time regarding plagiarism, Descartes was apparently unaware of
Snell's work.
Thus, in English speaking countries the law
of refraction is called ``Snell's law'', but in French speaking
countries
it is called ``Descartes' law''.

In 1658, the French mathematician Pierre de Fermat demonstrated that all
three of the laws of geometric optics can be accounted for
on the
assumption
that
light always travels between two points on the path which takes the
*least time* (or, more
rigorously, the extremal time). Fermat's ideas were an extension of those of Hero of
Alexandria. Fermat's (correct) derivation of the law of refraction
depended crucially
on his (correct) assumption that light travels *more slowly* in dense
media than it
does in air. Unfortunately, many famous scientists,
including Newton, maintained
that
light travels *faster* in dense media than it does in air. This
erroneous idea held
up progress in optics for over one hundred years, and
was not conclusively disproved until the mid-nineteenth
century.
Incidentally,
Fermat's principle of least time can only be justified
using
wave theory.