Chapter 1d

Hooke's Theory

by Edmund Taylor Whittaker

Hooke’s next effort was to produce a mechanical theory of refraction, to replace that given by Descartes.

Hooke says:

“All transparent mediums are not Homogeneous to one another.

How will this pulse or motion be propagated through differingly transparent mediums?

According to the most acute and excellent Philosopher Descartes, the sine of the angle of inclination in the first medium is the sine of refraction in the second, as the density of the first to the density of the second.

Density is not the density in respect of gravity (with which the refractions or transparency of mediums hold no proportion).

Density is in respect only to the trajection of the Rays of light, in which respect they only differ in this, that the one propagates the pulse more easily and weakly, the other more slowly, but more strongly.

But as for the pulses themselves, they will by the refraction acquire another property, which we shall now explicate.”

ACFD is a physical Ray. ABC and DEF are 2 mathematical Rays, trajected from a very remote point of a luminous body through an Homogeneous transparent medium LL, and DA, EB, FC, to be small portions of the orbicular impulses which must therefore cut the Rays at right angles.

These Rays meet with the plain surface NO of a medium that yields an easier transitus to the propagation of light.

Falling obliquely’ on it, they will in the medium MM be refracted towards the perpendicular of the surface.

This medium is more easily trajected than the former by a third, therefore the point U of the orbicular pulse FC will be moved to H four spaces in the same time that F, the other end of it, is inoved to 3 spaces, therefore the whole refracted pulse to H shall be oblique to the refracted Rays CHK and GI."

This is not in all respects successful.

But it advances the treatment of the same problem by Descartes, which rested on a mere analogy.

Hooke tries to determine what happens to the wave-front when it meets the interface between two media.

He introduces the correct principle that the side of the wave-front which first meets the interface will go forward in the second medium with the velocity proper to that medium.

The other side of the wave-front which is still in the first medium is still moving with the old velocity: so that the wave-front will be deflected in the transition from one medium to the other.

This deflection of the wave-front was supposed by Hooke to be the origin of the prismatic colours.

He regarded natural or white light as the simplest type of disturbance, being constituted by a simple and uniform pulse at right angles to the direction of propagation, and inferred that colour is generated by the distortion to which this disturbance is subjected in the process of refraction.

“The Ray [30] is dispersed, split, and opened by its Refraction at the Superficies of a second medium, and from a line is opened into a diverging Superficies, and so obliquated, whereby the appearances of Colours are produced.”

“Colour [31] is merely the disturbance of light by the communication of the pulse to other transparent mediums, that is by the refraction thereof.”

[32] “Blue is an impression on the Retina of an oblique and confused pulse of light, whose weakest part precedes, and whose strongest follows.

Red is an impression on the Retina of an oblique and confus’d pulse of light, whose strongest part precedes, and whose weakest follows.”

Hooke’s theory of colour was completely overthrown, within a few years of its publication, by one of the earliest discoveries of Isaac Newton (b. 1642, d. 1727).

Newton was elected a Fellow of Trinity College, Cambridge in 1667. He had in the beginning of 1666 obtained a triangular prism, “to try the celebrated Phaenomena of Colours.”

“Having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the Sun’s light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall.

It produced vivid and intense colours. I was surprised to see them in an oblong form. The received laws of Refraction saya they should have been circular.”

The length of the coloured spectrum was about 5 times as great as its breadth.

After more experiments, he discovered that ordinary white light is really a mixture of rays of every colour, and that the elongation of the spectrum is due to the differences in the refractive power of the glass for these different rays.

[33] I was forced from Cambridge by the intervening Plague"; this was in 1666, and his memoir on the subject was not presented to the Royal Society until five years later.

In it he propounds a theory of colour directly opposed to that of Hooke.

“Colours are not Qualifications of light derived from Refractions, or Reflections of natural Bodies (as ’tis generally believed), but Original and connate properties, which in divers Rays are divers.

Some Rays are disposed to exhibit a red colour and no other: some a yellow and no other, some a green and no other, and so of the rest.

Nor are there only Rays proper and particular to the more eminent colours, but even to all their intermediate gradations.

“To the same degree of Refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of Refrangibility:”

“The species of colour, and degree of Refrangibility proper to any particular sort of Rays, is not mutable by Refraction, nor by Reflection from natural bodies, nor by any other cause, that I could yet observe.

When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it.”

The publication of the new theory led to an acute controversy.

Hooke was foremost among the opponents, and led the attack with some degree of asperity.

At this time Newton was at the outset of his career.

Hooke was an older man, with an established reputation, such harshness appears particularly ungenerous.

Hooke charged him with holding the doctrine that light is a material substance.

Newton renounced the attempt to construct the universe from its foundations after the fashion of Descartes.

He merely aspired to formulate the laws which directly govern the actual phenomena.

His theory of gravitation, for example, is strictly an expression of the results of observation.

It involves no hypothesis as to the cause of the attraction which subsists between ponderable bodies.

His own desire in regard to optics was to present a theory free from speculation as to the hidden mechanism of light.

In reply to Hooke’s criticism, he protested[34] that his views on colour were in no way bound up with any particular conception of the ultimate nature of optical processes.

Newton was, however, unable to carry out his plan of connecting together the phenomena of light into a coherent and reasoned whole without having recourse to hypotheses.

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