A Source Book in Physics

Author: Étienne-Louis Malus

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Thus the characteristic which distinguishes direct light from that which has been subjected to the action of a crystal, is that the one may always be divided into two beams, while in the other this division depends on the angle contained between the plane of incidence and that of the principal section.

This power of changing the character of light and of giving to it a new property, which it carries with it, is not peculiar to Iceland spar; I have found it in all known substances which give double images. It is a remarkable thing about this phenomenon that it is not necessary, when we produce it, to use two crystals of the same sort. Thus the second crystal, for example, may be carbonate of lead, or sulphate of baryta: the first crystal may be a crystal of sulphur and the second rock crystal. All these substances behave in the same way as two rhomboids of calcspar. In general this disposition of light to be refracted in two beams or in one only depends only on the particular position of the axis of the integrating molecules of the crystals which we use, whatever may be otherwise their chemical origins and the natural or artificial faces at which refraction takes place. This result proves that the modification that light receives from these different bodies is perfectly identical.

In order to exhibit more plainly the phenomena which I have described, we may look at the flame of a candle through two prisms of different materials which give double refraction, set one over the other. We shall find in general four images of the flame; but if we slowly turn one of the prisms about the visual ray as axis, the four images are reduced to two, whenever the principal sections of the contiguous faces are parallel or perpendicular. The two images which disappear do not blend with the other two. We see them gradually extinguished while the others increase in intensity. When the two principal sections are parallel, one of the images is formed by the rays undergoing ordinary refraction in the two prisms, and the other image by the rays undergoing extraordinary refraction. When the two principal sections are at right angles, one of the images is formed by the rays refracted ordinarily by the first crystal and extraordinarily by the second, and the other image is formed by the rays refracted extraordinarily by the first crystal and ordinarily by the second.

Not only can all the crystals which give double images give to light this property of being refracted in two beams or in one according to the position of the refracting crystal, but all transparent bodies, solid or liquid, and even opaque bodies can impress on the molecules of light this singular disposition, which seems to be one of the effects of double refraction.

When a beam of light traverses a transparent substance, a part of the rays is reflected by the refracting surface and another part by the surface of emergence. The cause of this partial reflection, which hitherto has escaped the investigations of physicists, seems to have, in some respects, some analogy with the forces which produce double refraction.

For example, light reflected by the surface of water at an angle of 52° 45′ with the vertical has all the characteristics of one of the beams produced by the double refraction of a crystal of calcspar, of which the principal section is parallel or perpendicular to the plane which passes through the incident ray and the reflected ray and which we will call the plane of reflection.

If we receive this reflected ray on any crystal which has the property of doubling the images, and whose principal section is parallel to the plane of reflection, it will not be divided into two beams as a ray of direct light would have been, but it will be entirely refracted according to the ordinary law, as if the crystal had lost the power of doubling the images. If, on the other hand, the principal section of the crystal is perpendicular to the plane of reflection, the reflected ray will be entirely refracted according to the extraordinary law. In intermediate positions it will be divided into two beams following the same law and in the same proportion as if it had acquired its new character by double refraction. The ray reflected from the surface of the liquid has then in these conditions all the characteristics of an ordinary ray formed by a crystal whose principal section is perpendicular to the plane of reflection.

To analyze this phenomenon completely, I arranged a crystal with its principal section vertical and after I had divided a luminous ray by the aid of double refraction I received the two beams on the surface of water at the angle of 52° 45′. The ordinary ray, when it is refracted, gives up to partial reflection a part of its molecules, as a beam of direct light would have done, but the extraordinary ray enters the liquid completely; none of its molecules escape refraction. On the other hand, when the principal section of the crystal is perpendicular to the plane of incidence, the extraordinary ray only gives rise to partial reflection, and the ordinary ray is completely refracted.

The angle at which light experiences this modification when it is reflected at the surfaces of transparent bodies is different for each of them. In general it is greater for bodies which refract light more. Above or below this angle a part of the ray is more or less modified in a way analogous to that which occurs when light passes through two crystals whose principal sections are neither parallel nor perpendicular.

If we simply wish to examine this phenomenon without measuring it exactly, we place in front of a candle either the transparent body or the vessel containing the liquid upon which we are going to experiment. We look through a block of crystal at the image of the flame reflected at the surface of the body or of the liquid. We see in general two images; but by turning the crystal about the visual ray as an axis, we perceive that one of the images diminishes as the other increases in brightness. Beyond a certain limit the image which was enfeebled begins to increase in brightness at the expense of the other. We must determine approximately the point at which the intensity of the light is a minimum, and then move the candle nearer or further away from the reflecting body until the angle of incidence is such that one of the two images completely disappears; when this distance is determined, if we continue to turn the crystal slowly, we shall perceive that one of the two images is extinguished alternately at each quarter of a revolution.


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Chicago: Étienne-Louis Malus, "Polarization by Reflection," A Source Book in Physics in A Source Book in Physics, ed. William Frances Magie (Cambridge: Harvard University Press, 1935), 315–318. Original Sources, accessed December 6, 2022, http://www.originalsources.com/Document.aspx?DocID=LIPEGBQV8E5D2BP.

MLA: Malus, Étienne-Louis. "Polarization by Reflection." A Source Book in Physics, Vol. 2, in A Source Book in Physics, edited by William Frances Magie, Cambridge, Harvard University Press, 1935, pp. 315–318. Original Sources. 6 Dec. 2022. http://www.originalsources.com/Document.aspx?DocID=LIPEGBQV8E5D2BP.

Harvard: Malus, É, 'Polarization by Reflection' in A Source Book in Physics. cited in 1935, A Source Book in Physics, ed. , Harvard University Press, Cambridge, pp.315–318. Original Sources, retrieved 6 December 2022, from http://www.originalsources.com/Document.aspx?DocID=LIPEGBQV8E5D2BP.