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Encyclopedia Britannica - Main :: CAU-CHA |
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CAUSTIC (Gr. rcavvraubs, burning) , that which burns. In surgery, the term
malignant disease and gangrenous processes. Such substances are silver nitrate (lunar caustic
caustic
In optics, the term
bright curves when light is allowed to fall upon a polished riband of steel, such as a watch-spring , placed on a table, and by varying the form of the spring and moving the source of light, a variety of patterns may be obtained. The investigation of caustics, being based on the assumption of the rectilinear propagation of light, and the validity of the experimental laws
notably John Bernoulli, G. F. de I'Hbpital, E. W. Tschirnhausen and Louis Carre. The simplest case of a caustic curve is when the reflecting surface is a circle, and the luminous rays emanate from a point on the circumference. If in fig. 1 AQP be the reflecting circle caustics having C as centre, P the luminous point, and PQ any by incident ray, and we join CQ, it follows, by the law of the equality of the angles of incidence and reflection, that the reflection. reflected ray QR is such that the angles RQC and CQP are equal; to determine the caustic, it is necessary to determine the envelope of this line. This may be readily accomplished geometrically or analytically, and it will be found that the envelope is a cardioid (q.v.), i.e. an epicycloid in which the radii of the fixed and rolling
Elie Bocthor (17841821) was a French orientalist of Coptic origin. He was the author of a Traite des conjugaisons written in Arabic. and left his Dictionary in MS. remaining circular, the question can be similarly. treated, and it is found that the caustic is an epicycloid in which the radius of the fixed circle is twice that of the rolling
after any number of reflections at a spherical surface of rays, which are either parallel or diverge from a point on the circumference. In both cases the curves are epicycloids; in the first case the radii of the rolling and the fixed circles are a(2nI)/4n and a/2n, and in the second, an/(2n+I) and a/(2n+I), where a is the radius of the mirror and n the number of reflections. The Cartesian equation to the caustic produced by reflection at a circle of rays diverging from any point was obtained by Joseph Louis Lagrange; it may be expressed in the form +y2 (4c2a2)(x2~-y2)2a2cxa?c2}3 27a4c2y2(x2-c2)2, where a is the radius of the reflecting circle, and c the distance of the luminous point from the centre of the circle. The polar form is {(u+p) cos ZB} I+ {(up) sin 1B) a = (2k) a, where p and k are the reciprocals of c and a, and u the reciprocal of the radius vector of any point on the caustic. When c=a or =co the curve reduces to the cardioid or the two cusped epicycloid previously discussed. Other c=;5a c> a forms are shown in figs
Secondary caustics are orthotomic curves having the reflected or refracted rays as normals, and consequently the proper caustic curve, being the envelope of the normals, is their evolute. It is usually the case that the secondary caustic is easier to determine than the caustic, and hence, when determined, it affords a ready means for deducing the primary caustic. It may be shown by geometrical considerations that the secondary caustic is a curve similar to the first positive pedal of' the reflecting curve, of twice the linear dimensions, with respect to the luminous point. For a circle, when the rays emanate from any point, the secondary caustic is a limacon, and hence the primary caustic is the evolute of this curve. The simplest instance of a caustic by refraction (or diacaustic) is when luminous rays issuing from a point are refracted at a straight line. It may be shown geometric-ally that the secondary caustics caustic, if the second by mica,. medium be less refrac- don. tive than the first, is an ellipse having the luminous point for a focus , and its centre at the foot of the perpendicular from the luminous point to the refracting line. The evolute of this ellipse is the caustic required. If the second medium be more highly refractive than the first, the secondary caustic is a hyperbola having the same focus and centre as before, and the caustic is the evolute of this curve. When the refracting curve is a circle and the rays emanate from any point, the locus of the secondary caustic is a Cartesian oval
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