ON THE OPTICAL PROPERTIES OF A TITANO-SILICIC GLASS.

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been observed in the phosphatic series of glasses. Phosphatic glasses are too soft for convenient employment in optical instruments; but should titano-silicic glasses prove to be to silicic what titano-phosphatic glasses had been found to be to phosphatic, it would be possible, without encountering any extravagant curvatures, to construct perfectly achromatic combinations out of glasses having the hardness and permanence of silicic glasses; in fact the chief obstacle at present existing to the perfection of the achromatic telescope would be removed, though naturally not without some increase to the cost of the instrument. But it would be beyond the resources of the laboratory to work with silicic glasses on such a scale as to obtain them free from striæ, or even sufficiently free to permit of a trustworthy determination of such a delicate matter as the irrationality of dispersion.

When the subject was brought to the notice of Mr Hopkinson, he warmly entered into the investigation; and, thanks to the liberality with which the means of conducting the experiment were placed at his disposal by Messrs Chance Brothers, of Birmingham, the question may perhaps be considered settled. After some preliminary trials, a pot of glass free from striæ was prepared of titanate of potash mixed with the ordinary ingredients of a crown glass. As the object of the experiment was merely to determine, in the first instance, whether titanic acid did or did not confer on the glass the unusual property of separating the colours at the blue end of the spectrum materially more, and at the red end materially less, than corresponds to a similar dispersive power in ordinary glasses, it was not thought necessary to employ pure titanic acid; and rutile fused with carbonate of potash was used as titanate of potash. The glass contained about 7 per cent. of rutile; and as rutile is mainly titanic acid, and none was lost, the percentage of titanic acid cannot have been much less. The glass was naturally greenish, from iron contained in the rutile; but this did not affect the observations, and the quantity of iron would be too minute sensibly to affect the irrationality.

Out of this glass two prisms were cut. One of these was examined as to irrationality by Professor Stokes, by his method of compensating prisms*, the other by Mr Hopkinson, by accurate

[* Supra, p. 341

measures of the refractive indices for several definite points in the spectrum. These two perfectly distinct methods led to the same result—namely, that the glass spaces out the more as compared with the less refrangible part of the spectrum no more than an ordinary glass of similar dispersive power. As in the phosphatic series, the titanium reveals its presence by a considerable increase of dispersive power; but, unlike what was observed in that series, it produces no sensible effect on the irrationality. The hopes, therefore, that had been entertained of its utility in silicic glasses prepared for optical purposes appear doomed to disappointment.

P.S.-Mr Augustus Vernon Harcourt has now completed an analytical determination which he kindly undertook of the titanic acid. From 2:171 grammes of the glass he obtained ·13 gramme of pure titanic acid, which is as nearly as possible 6 per cent.

ON A PHENOMENON OF METALLIC REFLECTION.

[From the Report of the British Association for the Advancement of Science, Glasgow, 1876.]

THE phenomenon which I am about to describe was observed by me many years ago, and may not improbably have been seen by others; but as I have never seen any notice of it, and it is in some respects very remarkable, I think that a description of it will not be unacceptable.

When Newton's rings are formed between a lens and a plate of metal, and are viewed by light polarized perpendicularly to the plane of incidence, we know that, as the angle of incidence is increased, the rings, which are at first dark-centred, disappear on passing the polarizing angle of the glass, and then reappear white-centred, in which state they remain up to a grazing incidence, when they can no longer be followed. At a high incidence the first dark ring is much the most conspicuous of the series.

To follow the rings beyond the limit of total internal reflection we must employ a prism. When the rings formed between glass and glass are viewed in this way, we know that as the angle of incidence is increased the rings one by one open out, uniting with bands of the same respective orders which are seen beneath the limit of total internal reflection; the limit or boundary between total and partial reflection passes down beneath the point of contact, and the central dark spot is left isolated in a bright field*.

Now when the rings are formed between a prism with a slightly convex base and a plate of silver, and the angle of incidence is increased so as to pass the critical angle, if common light be used, in lieu of a simple spot we have a ring, which becomes more conspicuous at a certain angle of incidence well

[* Ante, Vol. 11, p. 358.]

beyond the critical angle, after which it rapidly contracts and passes into a spot.

As thus viewed the ring is, however, somewhat confused. To study the phenomenon in its purity we must employ polarized light, or, which is more convenient, analyze the reflected light by means of a Nicol's prism.

When viewed by light polarized in the plane of incidence, the rings show nothing remarkable. They are naturally weaker than with glass, as the interfering streams are so unequal in intensity. They are black-centred throughout, and, as with glass, they open out one after another on approaching the limit of total reflection and disappear, leaving the central spot isolated in the bright field beyond the limit. The spot appears to be notably smaller than with glass under like conditions.

With light polarized perpendicularly to the plane of incidence, the rings pass from dark-centred to bright-centred on passing the polarizing angle of the glass, and open out as they approach the limit of total reflection. The last dark ring to disappear is not, however, the first, but the second. The first, corresponding in order to the first bright ring within the polarizing angle of the glass, remains isolated in the bright field, enclosing a relatively, though not absolutely, bright spot. At the centre of the spot the glass and metal are in optical contact, and the reflection takes place accordingly and is not total. The dark ring, too, is not absolutely black. As the angle of internal incidence increases by a few degrees, the dark ring undergoes a rapid and remarkable change. Its intensity increases till (in the case of silver) the ring becomes sensibly black; then it rapidly contracts, squeezing out, as it were, the bright central spot, and forming itself a dark spot, larger than with glass, isolated in the bright field. When at its best it is distinctly seen to be fringed with colour, blue outside, red inside (especially the former), showing that the scale of the ring depends on the wave-length, being greater for the less refrangible colours. This rapid alteration taking place well beyond the critical angle is very remarkable. Clearly there is a rapid change in the reflective properties of the metal, which takes place, so to speak, in passing through a certain angle determined by a sine greater than unity.

I have described the phenomenon with silver, which shows it best; but speculum-metal, gold, and copper show it very well, while with steel it is far less conspicuous. When the coloured metals gold and copper are examined by the light of a pure spectrum, the ring is seen to be better formed in the less than in the more refrangible colours, being more intense when at its best; while with silver and speculum-metal there is little difference, except as to size, in the different colours. Hæmatite and iron pyrites, which approach the metals in opacity and in the change of phase which they produce by reflection of light polarized parallel relatively to light polarized perpendicularly to the plane of incidence, do not exactly form a ring isolated in a bright field; but the spot seen with light polarized perpendicularly to the plane of incidence is abnormally broad just about the limit of total reflection, and rapidly contracts on increasing the angle of incidence.

It seemed to me that a sequence may be traced from the rapidly contracting rings of diamond seen in passing the polarizing angle of that substance, through the abnormally broad and rapidly contracting spot seen with iron pyrites just about the limit of total reflection, and the somewhat inconspicuous ring of steel seen a little beyond the limit, to the intense rapidly contracting ring of silver seen considerably beyond the limit. If so, the full theory of the ring will not be contained in the usually accepted formulæ for metallic reflection, modified, as in the case of transparent substances, in accordance with the circumstance that the incidence on the first surface of the plate of air is beyond that of total reflection.

MacCullagh was the first to obtain the formulæ for metallic reflection, showing that they were to be deduced from Fresnel's formulæ by making the refractive index a mixed imaginary, though they are usually attributed to Cauchy, who has given formulæ differing from those of MacCullagh merely in algebraic detail. As regards theory, Cauchy made an important advance on what MacCullagh had done in connecting the peculiar optical properties of metals with their intense absorbing power*. Now Fresnel's formulæ do not include the phenomena discovered by

* The apparent difference between MacCullagh and Cauchy as to the values of the refractive indices of metals is merely a question of arbitrary nomenclature.