In this part, we will explore how the corpuscular theory of light and the wave theory of light
would each have their own champions and compete for ultimate success. We will discuss the
contributions made by the likes of Bernoulli, Young and Fresnel
In 1728 James Bradley attempted to determine the parallax of a star in the head of the
Dragon. What he discovered was that during the winter the transit across the meridian
was continually more southerly, while during the following summer its original position
was restored by a motion northwards. This effect could not be explained by parallax
but instead was caused by the gradual propagation of light. This discovery would therefore allow
astronomers to calculate the ratio of the mean orbital velocity of the earth to the
velocity of light, or, as it was called at the time, the constant of aberration.
From this Bradley was able to calculate the light took 8 minutes and 12 seconds to propagate
from the Sun to the earth.
With the exception of Bradley’s discovery, the eighteenth century was decidedly barren
in both experimental and theoretical investigations of light; which is in stark contrast to the
brilliance of the discoveries in electricity.
But it is worth pausing to consider an aether concept put forward by the younger John Bernoulli.
His idea seems to be built on top of the idea his father also named John Bernoulli had put
forward in 1701 which connected the law of refraction with the mechanical principle of
the composition of forces. If two opposing forces whose ratio is Mu maintained in equilibrium
a particle which is free to move only in a given plane, it follows from the triangle
of forces that the directions of the forces must obey the relationship sin i = mu sin
r
This is the same equation as that which expresses the law of refraction, and the elder Bernoulli
conjectured that a theory of light might be based on it but was never able to give any
satisfactory explanation for the existence of the forces. This would be done by his son.
His concept was that all space was permeated by a fluid aether, containing an immense number
of excessively small whirlpools. The elasticity of the aether allows it to transmit vibrations
largely because of these whirlpools. This he reasoned was due to the centrifugal force
each one possesses causing it to press upon the neighbouring ones, Throughout this medium,
there are small solid corpuscles who are much smaller than the distance they are apart.
They are pushed about by the whirlpools whenever the aether is disturbed but never travel far
from their original starting point.
A source of light communicates to its surroundings a disturbance that condenses the nearest whirlpools;
which then displaces the corpuscles from their equilibrium position. These in turn cause
the condensation of the next whirlpools. This way the vibrations are propagated in every
direction from the luminous point. What is curious is that Bernoulli defined these vibrations
as longitudinal but at the time Newton had already shown that the polarisation of light
ruled out longitudinal vibrations. What is impressive is that Bernoulli’s aether aside
from the longitudinal vibrations resembled the one Maxwell would come up with in 1861
for the express purpose of securing a transverse vibration. He so narrowly missed out on one
of the greatest discoveries.
Not long after this, the controversy of refraction that pitted Descartes against Fermat would
be re-awakened by Pierre-Louis-Moreau de Maupertuis. The main argument between these two was regarding
the speed of light.. Descartes thought it would be greatest in a dense medium whereas
Fermat thought the light would travel at its fastest in free aether.
Maupertuis thought that Descartes was right but wished to retain Fermat’s beautiful method. So
he proposed that instead of assuming light follows the quickest path, he felt it should
be that it follows the path described by which the quantity of action is the least. So instead
of Fermat’s expression where t denotes time, v velocity and ds is an element of the path
Maupertuis defined it as follows
What is important to realise is that in this case, v represents the velocity according
to the corpuscular theory which is proportional to the reciprocal of Fermat’s v which denotes
the velocity according to the wave theory. This means the two expressions are really
equivalent.
The important point of his work is more about the dynamics. His suggestions were subsequently
developed further by himself and Euler and Lagrange into a general principle that covers
the whole range in Nature.
Most of the natural philosophers of the eighteenth century for the most part accepted the corpuscular
hypothesis.
There were some who would defend the wave theory, these would include the likes of Benjamin
Franklin and Leonhard Euler. Both saw a problem with the idea that the emission of particles
would cause a decrease in the mass of the radiating body, which had not been observed.
In contrast, the wave theory had no such consequence.
In a series of letters Euler wrote he set forth his view on natural philosophy. He anticipated
Maxwell in asserting that the source of all electrical phenomena is the same aether that
propagates light. Electricity in his view was nothing but a derangement of the equilibrium
of the aether. A body must become electrical he said whenever the aether contained in its
pores becomes more or less elastic than that which is lodged in adjacent bodies. This happens
when a greater quantity of aether is introduced into the pores of the body or when the either
contained within it is forced out. The effort it makes to recover the equilibrium with the
surrounding, produce all the phenomena of electricity. In his view, a single aether
would account for all the phenomena including gravity.
The fortunes of the wave theory started to brighten by the end of the century when a
new champion arose. Thomas Young began writing his optical theory in 1799. He outlined a
superior theory to explain reflection and refraction. In particular, it was able to
explain why light would be partially reflected of certain objects and was analogous to the
partial reflection of sound from a cloud or denser stratum of air. Refracting media would
contain a denser quantity of luminous ether compared to a vacuum but would not affect
its elasticity.
Young’s greeted discovery would come in 1801 when he was attempting to explain Newton’s
rings using the principles of wave theory. The concept he used had originally been put
forward by Newton in his theory of tides. He had stated that the tide may propagate
from the ocean through different channels towards the same port, and may pass in less
time through some channels than through others. The effect by the composition of these would
generate new types of tides.
Young used the analogy of the lake to make his point. Suppose a number of equal waves
of water move upon the surface of a stagnant lake, with a certain constant velocity, and
enter a narrow channel leading out of the lake. Now suppose another similar series of
waves are excited in the lake, which arrives at the same channel, with the same velocity,
and at the same time as the first. Neither series of waves will destroy each other but
their effects will combine. Where wave peaks meet they will combine and where a trough
meets a peak they will create a smooth surface. His view was that a similar effect takes place
whenever two portions of light are mixed. This he called the general law of interference
of light.
Young’s explanation of the colours of thin plates as by reflection arises from the fact
that the incident light gives rise to two beams that reach the eye: one of these beams
is reflected at the first surface of the plate and the other at the second surface and these
two beams produce the colours by their interference.
The first publication of Young’s paper received a fierce attack from Henry Brougham, who later
became the Lord Chancellor of England. So intense was this attack that Young failed
to make any impression with his ideas in the ensuing years.
Young ploughed on and investigated fringes of shadows and then would turn his attention
to the behaviour of light in crystals which was last looked at by Huygens more than a
century earlier.
Meanwhile, the corpuscular theory was also making good progress and was likely to undermine
Young’s work. The first of these was a dynamical explanation of the refractions of light inside
a crystal which was published in 1808 by Laplace. His method was an extension of the work of
Maupertuis. His concept was that the crystalline medium acts on the light corpuscles of the
light rays so as to modify their speed in a ratio that depended on their inclination
to the axis of the crystal.
Young promptly attacked the idea by pointing out the improbability of such a system of
forces that would be required to impress the requisite change of velocity on the light
corpuscles.
Meanwhile, in January 1808 Etienne-Louis Malus made a discovery while observing the sun setting
through a crystal of Iceland spar reflected from a window. He noticed that the two images
were of very different intensities. He went on to discover that light which had been refracted
at the surface of any transparent substance likewise posses in some degree this same property
to which he gave the name polarisation.
The wave theory at this time was struggling. Diffraction was not properly explained. Polarisation
had no explanation.
The upholders of the corpuscular theory were emboldened by this and proposed Diffraction
as the next topic for the Academy’s prize of 1818. This would spell the end and the
winning paper would signal a series of reversals that would see the corpuscular theory totally
overthrown.
The author of this paper was Augustin Fresnel. In 1816 he presented his paper where he outlined
that diffraction effects were caused by the mutual interference of the secondary waves
emitted by those portions of the original wavefront which have not been obstructed by
the diffracting screen. Fresnel’s method of calculation utilised the principles of
both Huygens and Young. This original paper would over the next two years be developed
into a memoir that would need a champion as Laplace, Poisson and some others supported
the corpuscular theory and occupied the majority of the commission.
Poisson when reading this manuscript noticed his analysis could be extended to include
other cases. He suggested this to Fresnel who would later confirm this experimentally
and confirmed this new theory. The concordance of observation and calculation was so admirable
in all cases where a comparison was possible that the prize was awarded to Fresnel without
further hesitation.
In the same year, Fresnel also published an investigation into the influence of the earth’s
motion on light. He viewed that the light aether pervades the substance of all material
bodies with little or no resistance. He viewed that the aether surrounding the earth to be
at rest and unaffected by the Earth’s motion. This gave rise to a series of further questions.
What is a slab of glass with a place face is carried along by the motion of the earth,
and it is desired to adjust it so that a ray coming from a certain star will not be refracted
when entering the glass, should the surface be placed at right angles to the true direction
of the star as freed from aberration, or to its apparent direction as affected by aberration?
This question had initially been raised by Mitchell.
Argo submitted the matter to the test and concluded that the light coming from any star
behaves in all cases of reflection and refraction precisely as it would if the star were situated
in the place which it appears to occupy due to aberration as if the earth were at rest
so that the apparent refraction in a moving prism is equal to the absolute refraction
in a fixed.
Fresnel now set out to provide a theory capable of explaining Arago’s result. To this end,
he adopted Young’s suggestion, that the refractive powers of transparent bodies depend
on the concentration of aether within them and made this proportional to the square of
the refractive index.
He also assumed that when a body is in motion, the part of the aether whose density was above
that in a vacuum would be carried along with it while the rest would be stationary.
Fresnel then proceeded to solve the problem of refraction in moving bodies. He showed
that the apparent positions of terrestrial objects, carried along with the observer,
are not displaced by earth’s motion; that experiments in refraction and interference
are not influenced by any motion which is common to the source, apparatus and observer;
and that light travels between given points of a moving material system by the path of
least time.
The greatest problem now confronting the investigators of light was to reconcile the facts of polarisation
with the principles of the wave theory. In 1816 Young received a visit from Arago, who
told him of new experimental results which showed that two beams of polarised light in
planes at right angles to each other do not interfere with each other where ordinary light
would.
Young finally had the key to understanding the problem. The solution consisted of the
alternative which Bernoulli had rejected eighty years before. The vibrations of light are
executed at right angles to the direction of propagation.
It must be remembered that the theory of propagation of waves in an elastic solid was as yet unknown,
and light was still always interpreted by the analogy with the vibrations of sound in
air, for which the direction of vibration is the same as that of propagation.
Fresnel felt it important to explain this new departure. With wonderful insight, he
said ‘the geometers who have discussed the vibrations of elastic fluids hitherto have
taken account of no accelerating forces except those arising from the difference of condensation
of dilatation between consecutive layers. He pointed out that if we also suppose the
medium to possess a rigidity, or power of resisting distortion, such as is manifested
by all actual solid bodies, it will be capable of transverse vibration. The absence of longitudinal
waves in the aether he accounted for by supposing that the forces which oppose condensation
are far more powerful than those which oppose distortion, and that the velocity with which
condensations are propagated is so great compared with the speed of the oscillations of light,
that a practical equilibrium of pressure is maintained perpetually.
Fresnel also outlined the difference between ordinary and polarised light as follows. Direct
light can be considered as the union, or more exactly as the rapid succession, of systems
of waves polarised in all directions. According to this way of looking at the matter, the
act of polarisation consists not in creating these transverse motions, but in decomposing
them into two invariable directions, and separating the components from each other; for then,
in each of them, the oscillatory motions take place always in the same plane.
By the genius of Young and Fresnel, the wave-theory of light was established in a position so
strong that from the point onwards the corpuscular hypothesis was unable to attract any new talent
to further it.
In the next part, we will explore how this shaped the idea that the aether had to be
an elastic solid.