The simplest way of showing dispersion is to refract a narrow beam of sunlight through a prism of glass or prismatic vessel containing water or other clear liquid. As the light is twice refracted, the dispersion is increased, and the rays, after transmission through the prism, form a divergent system, which may be allowed to fall on a sheet of white paper, forming the well-known solar spectrum. This method was employed by Sir Isaac Newton, whose experiments constitute the earliest systematic investigation of the phenomenon. Let O (fig. 2) represent a small hole in the shutter of a darkened room, and OS a narrow beam of sunlight which is allowed to fall on a white screen so as to form an image of the sun at S. If now the prism P be interposed as in the figure, the whole beam is not only refracted upward, but also spread out into the spectrum RV, the horizontal breadth of the band of colours being the same as that of the original image S. In an experiment similar to that here represented, Newton made a small hole in the screen and another small hole in a second screen placed behind the first. By slightly turning the prism P, the position of the spectrum on the first screen could be shifted sufficiently to cause light of any desired colour to pass through. Some of this light also passed through the second hole, and thus he obtained a narrow beam of practically homogeneous light in a fixed direction (the line joining the apertures in the two screens). Operating on this beam with a second prism, he found that the homogeneous light was not dispersed, and also that it was more refracted the nearer the point from which it was taken approached to the violet end of the spectrum RV. This confirmed his previous conclusion that the rays increase in refrangibility from red to violet.
| Fig. 3.—Method of Crossed Prisms. |
Newton also made use of the method of crossed prisms, which has been found of great use in studying dispersion. The prism P (fig. 3) refracts upwards, while the prism Q, which has its refracting edge perpendicular to that of P, refracts towards the right. The combined effect of the two is to produce a spectrum sloping up from left to right. The spectrum will be straight if the two prisms are similar in dispersive property, but if one of them is constructed of a material which possesses any peculiarity in this respect it will be revealed by the curvature of the spectrum.
The coloured borders seen in the images produced by simple lenses are due to dispersion. The explanation of the colours of the rainbow, which are also due to dispersion, was given by Newton, although it was known previously to be due to refraction in the drops of rain (see [Rainbow]).
According to the wave-theory of light, refraction (q.v.) is due to a change of velocity when light passes from one medium to another. The phenomenon of dispersion shows that in dispersive media the velocity is different for lights of different wave-lengths. In free space, light of all wave-lengths is propagated with the same velocity, as is shown by the fact that stars, when occulted by the moon or planets, preserve their white colour up to the last moment of disappearance, which would not be the case if one colour reached the eye later than another. The absence of colour changes in variable stars or in the appearance of new stars is further evidence of the same fact. All material media, however, are more or less dispersive. In air and other gases, at ordinary pressures, the dispersion is very small, because the refractivity is small. The dispersive powers of gases are, however, generally comparable with those of liquids and solids.
Dispersive Power.—In order to find the amount of dispersion caused by any given prism, the deviations produced by it on two rays of any definite pure colours may be measured. The angle of difference between these deviations is called the dispersion for those rays. For this purpose the C and F lines in the spark-spectrum of hydrogen, situated in the red and blue respectively, are usually employed. If δF and δC are the angular deviations of these rays, then δF − δC is called the mean dispersion of the prism. If the refracting angle of the prism is small, then the ratio of the dispersion to the mean deviation of the two rays is the dispersive power of the material of the prism. Instead of the mean deviation, ½ (δF + δC), it is more usual to take the deviation of some intermediate ray. The exact position of the selected ray does not matter much, but the yellow D line of sodium is the most convenient. If we denote its deviation by δD, then we may put
Dispersive power = (δF - δC)/δD (1).
This quantity may readily be expressed in terms of the refractive indices for the three colours, for if A is the angle of the prism (supposedly small)
δC = (μC − 1)A, δD = (μD − 1)A, δF = (μF − 1)A,
where μC, μD, μF are the respective indices of refraction. This gives at once