104 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



Essay on Sciences for the theory of double refraction, Malus 

 double re- wro ^ e a se cond paper, which was crowned, but which, 

 however admirable as a specimen of mathematical 

 address, added little to what was previously known. 

 (479.) Malus had already, in the end of 1808, announced 

 Huygens' a property of light which, if not absolutely new, was 

 discovery en ^j re iy so w jth reference to the circumstances in 

 ofpolariza- I . , *. n j mi i . T i 



tion by calc which it was produced. The polarization of light 



spar. was in reality discovered by Huygens previous to 



1680. He had observed that the two rays into which 

 common light is divided in passing through Iceland 

 spar have a singular diversity of character, which 

 Newton afterwards described as an opposite polarity. 

 Huygens showed that if two rhombs of doubly re- 

 fracting spar are laid symmetrically one upon the 

 other, the " extraordinary" ray yielded by the first is 

 extraordinarily refracted by the second, and the "ordi- 

 nary" ray from the first is ordinarily refracted by the 

 second. But when we revolve the upper rhomb 

 as it lies upon the lower one through a right angle, 

 a remarkable change appears. The extraordinary 

 ray escaping from the first is now ordinarily re- 

 fracted by the second, and vice versa, so that the 

 qualities of the two rays differ but only so far as this, 

 that either may be assimilated to the other by making 

 it (or the crystal from which it derives its properties) 

 revolve round ninety degrees. A definite notion of 

 such a distinction may be formed by imagining a 

 musical string vibrating at one time in a vertical, at 

 another in a horizontal, plane. If we could possibly 

 imagine light to consist of vibrations of this descrip- 

 tion, the two rays of Iceland spar might be conceived 

 the one to vibrate in a plane passing through the 

 axis of the crystal, the other in a plane perpendicular 

 to that. Such light might truly be said to have ac- 

 quired the property of having sides. In the language 

 of Newton, it is polarized. 



(480.) The discovery of Malus consisted in showing that 

 Malus dis- light may acquire properties identical with those of 

 larization" e ^ er ray yielded by refraction through Iceland spar, 

 by reflec- by the very simple process of simple reflection at a par- 

 tion. ticular angle from any transparent body. Thus for a 



surface of water he found this angle to be 52 45' with 

 the perpendicular, and for glass 54 35'. The reflected 

 light in either case has exactly the property of the or- 

 dinary ray transmitted by a crystal whose principal sec- 

 tion (that is, a section passing through the axis of the 

 crystal) is parallel to the plane of reflection. Con- 

 sequently this light will be acted on by a doubly re- 

 fracting crystal placed in its way precisely as if it 

 had emerged from a similar crystal; and, on the 

 other hand, if the two rays emerging from a crystal 

 be incident on water or glass as above mentioned, the 

 one will be copiously reflected from the surface, whilst 

 the other will not be reflected at all, but pass entirely 

 into the transparent substance. Farther, as might 

 be expected, light thus polarized by reflection, when 



it falls on a second similar reflecting surface at the 

 same angle as before, will be copiously reflected if the 

 planes of reflection coincide, but will refuse to be 

 reflected in an appreciable degree when the planes of 

 reflection are perpendicular. 



This phenomenon was detected by Malus by casually (481 .) 

 observing that a ray from the setting sun reflected Occasion 

 from a distant window, and viewed through a piece lt- 

 of Iceland spar, afforded but a single image in two 

 positions of the latter. The experiment attracted uni- 

 versal attention, and became the germ of a series of 

 optical discoveries almost unprecedented for their 

 beauty and variety ; yet most of the experiments may 

 be made quite as well when light is polarized by the 

 method of Huygens as by that of Malus. Neverthe- 

 less the former had remained a sterile fact for 1 30 

 years. Upon such trifling circumstances does the 

 progress of knowledge often depend. 



Malus survived his discovery only four years, and (432.) 

 saw but the borders of that land of promise which he Law of t: 

 had pointed out to others. A few results he however cosines * 

 obtained, which are worthy of notice. Thus he found 

 that in every instance where light is polarized in any 

 plane there is also produced a certain proportional 

 amount of light polarized in the perpendicular plane. 

 Arago afterwards proved the very important fact, that 

 these two portions are universally equal. Huygens 

 had shown in the experiment of the two rhombs, that 

 when their positions are neither symmetrical nor 

 perpendicular, each ray emerging from the first is 

 duplicated by the second. When the principal sec- 

 tions of the rhombs are inclined 45, the duplicated 

 rays are equally bright ; as they approach parallelism 

 or perpendicularity, one pair of the rays brighten and 

 the other pair is enfeebled. Malus ascertained the 

 law of change of brightness, which is the same for 

 rhombs of spar or for plates of glass whose planes 

 of reflection vary whilst the angle of reflection re- 

 mains constant. In either case the intensity of the 

 light varies as the square of the cosine of the angle 

 formed by the principal sections of the crystals or 

 the planes of reflection of the plates. This impor- 

 tant law, the best established in photometry, has been 

 applied by Arago to the measurement of light in 

 many instances, but the details were unfortunately 

 not made public before his decease. 



To Malus is also due the discovery of the polariza- (483.) 



tion of light by common refraction. When light is in- Other dis 

 'j , i ' .-I D-J.J-I ,. coveries. 



cident on glass or water, the refracted beam contains 



precisely as much polarized light as the reflected beam, 

 but oppositely polarized. The metals were at first 

 believed by Malus to polarize no appreciable quan- 

 tity of light. He afterwards found that at great in- 

 cidences the reflected light is partly polarized. 1 He 

 likewise ascertained the fact of the "depolarization" (as 

 it was termed) of light by many crystals, and also by 

 organized substances, such as hair, horn, and whale- 



1 See an interesting letter from Malus to Dr Young in Thomson's Annals, vol. Hi. 



