LIGHT 593 markable results were obtained by Blair,[1] with two glass lenses enclosing a lenticular portion of a liquid.
Lines in the solar spectrum.
By looking through a prism at a very narrow slit, formed by the window shutters of a darkened room, Wollaston (in 1802 ) found that the light of the sky (i.e., sunlight) gives a spectrum which is not continuous. It is crossed by dark bands, as already hinted. These bands are due to the deficiency of intensity of certain definite kinds of homogeneous light. They were, independently, redis covered, and their positions measured, by Fraunhofer[2] in 1817 with fur more perfect optical apparatus. He also found similar, but not the same, deficiencies in the light from various fixed stars. The origin of these bands will be explained ie RADIATION, along with the theory of their application in spectrum analysis. In optics they are useful to an extreme degree in enabling us to measure refractive indices with very great precision. Wollaston's own account of his discovery is as follows: –
" If a beam of day-light be admitted Into a dark room by a
crevice ^Vth of an inch broad, and received by the eye at the distance
of 10 or 12 feet, through a prism of flint-glass, free from veins,
held near the eye, the beam is seen to be separated into the four
following colours only, red, yellowish-green, blue, and violet, in
the proportions represented in fig. ...
"The line A that bounds the red side of the spectrum is some what confused, which seems in part owing to want of power in the eye to converge red light. The line B, between red and green, in a certain position of the prism is perfectly distinct ; so also are D and E, the two limits of violet. But C, the limit of green and blue, is not so clearly marked as the rest ; and there are also on each side of this limit other distinct dark lines f and g, either of which in an imperfect experiment might be mistaken for the boundary of these colours.
"The position of the prism in which the colours are most clearly divided is when the incident light makes about equal angles with two of its sides. I then found that the spaces AB, BC, CD, DE occupied by them were nearly as the numbers 16, 23, 36, 25. " 3
The mode of formation of a spectrum which was employed by Newton, and which is still used when the spectrum is to be seen by many spectators at a time, differs from that just explained in this, that the light from a source A is allowed to pass through the prism, and to fall on a white screen at a considerable distance from it. In this case the paths of the various rays as they ultimately escape from the prism are found by joining the points r,. . . . v, with the prism and producing these lines to inpure meet the screen. Unless one surface of the prism be pectrum. covered by an opaque plate, with a narrow slit in it parallel to the edge of the prism, the spectrum produced in this way is very impure, i.e., the spaces occupied by the various homogeneous rays overlap one another. To make it really pure an achromatic lens is absolutely re quisite. This leads us, naturally, to the consideration of the refraction of light at spherical surfaces. Spherical Refraction at a Spherical Surface. Following almost exactly the same course as that taken with reflexion above, let O (fig. 15) be the centre of curvature of the spherical refracting surface AB. Let U be the point-source of homogeneous light, and let PV be the prolongation (back wards) of the path pursued, after refraction, by the ray UP.
1 Trans. R.S.E., vol. iii. (1791).
2 Gilbert's Annalen, lvi.
3 "The correspondence of these lines with those of Fraunhofer I have, with some difficulty, ascertained to be as follows: –
A, B, f, C, g, D, E, . . . Wollaston's lines. B, D, b, F, G, H, . . . Fraunhofer's lines.
There is no single line in Fraunhofer's drawing of the spectrum, nor is there any in the real spectrum, coincident with the line C of Wol laston's, and indeed he himself describes it as not being 'so clearly marked as the rest.' I have found, however, that this line C corre sponds to a number of lines half-way between b and F, which, owing to the absorption of the atmosphere, are particularly visible in the light of the sky near the horizon." – Brewster, Report on Optics, Brit. Association, 1832.
Then, rigorously, we have
sin UPO=/iSin OPV,
where //, is the index of refraction between the two media
employed. This may be written (by omitting a common
factor) as
o u _ oy
PU " M PV
If, as before, the breadth of the surface be small cmn-
pared with its radius of curvature, we may approximate
(sufficiently for many important practical purposes) by
writing A for P. Thus we have
OU _ 0V
AU " M AV
Retaining the same notation as in the case of reflexion,
we get
or
(D.
Notice that, if we put μ = -1, this becomes the formula
for reflexion at a concave mirror.
Lenses. – Suppose now that, after passing a very short Thin distance into the refracting medium, the ray escapes again lense into air through another spherical surface whose centre of curvature also lies in the line OA. Let s be the new radius of curvature, w the value of the quantity corresponding to v for the escaping ray. Then, remembering
that the refractive index is now _,we have (by the previous formula) - 1 or Adding (1) and (2) we get rid of v, which indicates the behaviour of the rays in the substance of the lens, and have This contains the whole (approximate) theory of the behaviour of a very thin lens. When the source is at an infinite distance, or u= oo, we have = suppose.
This quantity f, defined entirely in terms of the refractive index and of the curvatures of the two faces of the lens, is called the principal focal distance. If μ be greater than 1, i.e., as in the case of a glass lens in air, f is positive if
r s
Reversibility of thin lens.
be so; and it obviously retains the same value, and sign, if the lens be turned round. For, in the formula, r and s change places, and they also change signs; i.e., we must
