REF
CpSo)
R£P
But Note, the Attraction of the dcnfer Medium, e. gr. N, is Continually diminifhing as the Ray proceeds from B, towards the limit of Attraction RT$ in regard fewer and fewer Parts ftiU come to aS : at IH, e. gr. all the Parts between that and PS at- tract, but at RT, none but thofe in the Line HI.— Note alfo, that the Diftance between PS and RT being fmall, when we conlider Refractions, no Notice is taken of the Curve Part of the Ray; but we confider it as conliftingof two ftraight Lines, CB, AB, orwB, AB.
Refraction, in Dioptricks, is the Inflection or bending ot the Rays of Light, in paffmg the Surfaces of GlafTes, Lernes, and other tranfparent Bodies of different Denfuies.
Thus a Ray, as AB, {Tab. Opticks, Fig. 56.) falling obliquely from the Radiant A, upon a Point B, in a diaphanous Surface, HI rarer or denfer than the Medium along which it was propagated from the Radiant; it has its Direction there alter'd by the Acti- on of the new Medium, and initead of proceeding to M deviates, e. gr. to C.
This Deviation is called the Refraction of the Ray: BC the Refracled Ray, or Line of Ref ratlion; and B the Point of Re- fradion. Sec Ray, Line, and Point.
The Line AB is call'd the Line of Incidence-, or Ray of l?ici- aence; and in refpect hereof B is alio called the Point of Incidence. See Incidence.
The Plane wherein both the incident and reflecledRzys are found, is called the Plane of Refraction; a right Line BE drawn in the refracting Medium perpendicular to the refracting Surface in the Point of Refraction B, is call'd the Axis of Refraction— And a right Line DB drawn perpendicular to the refracting Surface, in the Point of Incidence B, along the Medium through which the Ray fell, is called the Axis of Incide?ice. See Plane, Axis,
The Angle AB[ included between the incident Ray, and the refratling Surface, is called the Angle of Incidence $ and the Angle ABD included between the incident Ray, and the Axis of Inci- dence, is call'd the Angle of Inclination— The Angle MDC which the refracted Ray makes with the Incident, is call'd die Angle of Refraction ; and the Angle CBE which the refracted Ray makes with the Axis of Refraction, is call'd the refracled Angle. See Angle.
General Law of Refraction.
I. A Ray of Light in its Pajfage out of a rarer, into a denfer Medimn-i e. gr. out of Air into Glafs, is refracled towards the Per- pendicular , i. e. towards the Axis of Refraction.
Hence, the refracted Angle is lefs than the Angle of Inclinati- on ; and the Angle ot Refraction lefs than that of Incidence ; as they would be equal, were the Ray to proceed ftraight from A to M.
Hence, alfo a Ray perpendicular to the refracting Surface, will pals through without being refracted; as it cannot be refraled to the Perpendicular. The phyfical Caufe thereof is, that the At- traction of the denfer Medium, which in Incidences oblique to its Surface acting perpendicular to that Surface, draws the Ray out ot its Courfe: This Attraction, we fay, in a perpendicular Incidence, ads in the Direction of the Ray.
II. Th? Ratio of the Sin? of the Angle of Inclination^ to the Sim of the refracted A?igle 7 is fix d and conflant ; viz. If the Refraction be out of Air into Glafs, it is found greater than as 114 to 76; but lefs than 1 15 to 76; that is, nearly as 3 to 2.
This Ratio, affign'd by Huygens, agrees with another of Sir Ifaac Newto?i, who makes the Sine of the Angle of Inclination to the Sine of the refracled Angle, as 3 1 to 20 ; which is, like- wile, nearly as 3 102..— Indeed there is fome Difference in the Quantity of RcfraUion, in different Kinds of Glafs ; but in phy- fical Matters, Precifenefs is not neceflary. — In Rain Water, D?s Cartes found, the Ratio of the Sine of the Angle of Inclination, to the Sine of the refracled Angle, as 250 to 187, that is, near- ly as 4 to 3 ; which agrees with Sir Ifaac Newton's Observation, who makes it as 529 to 395. — In Spirit of Wine, the fame great Author makes (he Ratio as 100 to 73 j which is not far from the fefqui tertian Ratio.— In Air he makes it as 3851 to 3850.
Whence the different refractive Power in different Fluids arifes, is not determined.— Clear Water, of all others, refracts theleaft; and \S impregnated with Salts, its Refraction is increafed in Pro- portion to the Quantity of Salt. Sir Ifaac Newton fhews, that in many Bodies, e. gr. Glafs, Cryftal, a Selenites, Pfeudo-To- paz, &c- the refradi-ve Power is proportionable .to their Denlities,- only in fulphurous Bodies, as Camphire, Oil Olive, Amber, Spi- rit of Turpentine, &c. the Power is two or three times greater than in other Bodies of equal Denficy ; yet they have the Refractive Power with refped to each other, nearly as their Denfities. — As to Air, he fhews that a Ray of Light in traverfing quire thro' the Atmofphere, is refracled the fame it would be were it to pafs with the fame Obliquity out of a Vacuum into Air of equal Denfity with that in the loweftPart of the Atmofphere. See Air.
From the Law juft laid down, it follows that one Angle of In- clination, arid its correfpondingre/Witf.'^Angle being found by Ob- fervation; the refracled Angles correfponding to the feveral other Angles of Inclination, are eafily computed.— Now, Zahnius and Either have found, that if the Angle of Inclination be 70°. the
refracled Angle will be 38' 50'; on which Principle Zahnius hai conftrudted a Table of Refractions out of Air into Glafs, for the feveral Degrees of the Angle of Inclination:; a Specimen wherer of follows.
Ang. of
Refracted
Angle or
rtiig.on Kelracuu | /ingle ot |
Inclin.
Angle.
Refraction.
Inclin. I _ Angle. |Refraflion |
l a
o» 4 o'5"
0" I9'55
lo a
0' 39 10"
3-20 44-'
2
1 20 6
13 54
20
13 n 35
6 48 25
3
2 3
59 5S
3°
19 29 29
10 30 31
4
2 40 5
t 19 55
45
28 9 19
16 50 41
5
3 20 3
1 39 57
90 41 <p 40
4S 8 20
Hence it appears that at an Angle of Inclination lefs than 20 the Angle of Refraction out of Air into Glafs, is almoft ~ of the Angle of Inclination : And therefore a Ray is refraCld to the Axis of Refraction, by almoft a third Part of the Quantity of its Angle of Inclination —And on this Principle it is that Kepler and molt other dioptrical Writers, demonftrate the Refraclions'm Glaffcs.
The conftmt Ratio of the Sines of the Angles of Inclination, and the refracted Angles was firft difcovcred by Wilkb. Snellius. — 'Tis vulgarly attributed to Des Cartrs ; .who having feen it in Snellius's MS, firft publifhcd it in his Dioptricks, without na- ming Snellius ; as we are inform'd by Huygens.
Indeed, as the Rays of Light are not all of the fame Degree ot Refrangibility ; this conflant Ratio mult be different in diffe- rent Kinds. — The Ratio therefore obferved by Au.hors is to be underftood of Rays of the mean Ref tangibility, i. c. of green Rays. The Difference of Refraction between the lead and molt refrangible Rays, that is between Violet and red Rays, Sir Ifaac Newton fhews is about £, Part of the whole Refaction of the mean Refrangible; which Difference he owns is lb fmall, that there feklom needs to be any regard had to it. See Refran-
GIBILITY.
III. Vyhen a Ray pajfes out of a denfr into a ra v er Medium, e. gr. out of Glafs into Air, it is refracted from the Perpendicular, or from the Axis of Refraction.— And hence the Angle of Refraction is greater than the Angle of Inclination.
Hence, alfo, if the Angle of Inclination be lefs than 30 ; MBC is nearly equal to i of MBE.— Therefore MBC is one half of CBE : Confequently, if the Refraclion be out of Glafs into Air,' and the Angle of Inclination lefs than 30 ; the Ray is refracted from the Axis of Refraction by almoft one half Pare of the Angle of Inclination.— And thus is the other dioptrical Principle ufed by mod Authors after Kepler, to demonftrate the Refractions of Glafies.
If the Refraction be out of Air into Glafs, the Ratio of the Sine of Inclination to the Sine of the refracted Angle is as 2 to 3 ; if out of Air into Water, as 4 to 3 : Therefore, if the Re- fraction be the contrary way, viz. out of Glafs or Water into Air; the Ratio of the Sines in the former Cafe, will be as 2 to 3, in the latter as 4 to 3.
IV. A Ray falling on a Curve Surface, whether Concave or Con- vex; is refract 'd after the fame Manner as if it fell on a Plans ivhich is a Tangent to the Curve in the Point of Incipience.
For the Curve and plain Surface touching it, have an infinite- ly fmall Part common to ihcm both, (each being originally gene- rated by the Flux of a Point). But a Ray is refrcd:d in fuch a little Part; therefore 'tis the fame as if it were refreded in fuch a Plane. J
V. If A right Line EF (Fig. 57. and ;3.) cut a refracting Sur- face GH at right Angles ; and if from any Point in the denfer Medium as D be drawn DC Parallel to the incident Ray AB : This veill meet the refrr. Bed Ray in C ; and will be to it as the Sine of the re- fracted Angle to the Sine of the A?tgle of Inclination.
Hence, if BC pafs out of Glafs into Air, it is in a fubfefquial- terate Ratio to CD ; if out of Air into Glafs, in a lefquialtera'e Ratio to CD. H
Hence, alfo, if Light pafs out of Water into Air ; CB is in a fubfefquitertian Ratio to CD ; if out of Air into Water in a Sef- quiquartan.
Z.^'Uir of Refraction in Plane Surfaces.
l°.If parallel Rays be refracted out of one tranfparent Body into another of different Denlity, they will continue Parallel after Re- fraction.
The phyfical Reafon is, rhat being parallel, their Obliquity, or Angle of Incidence is the fame : But at equal Obliquities we have fhewn the RefraClion is equal ; confequenily the Parallelifm which they had before the RefraClion, will be reraih'd after it.
But this may be alio demonftrated Geometrically, thus: If the Rays be perpendicular to the refracting Surface, they will pals without any Refraction ; coniequemly being parallel before their Paffage, they will be fo after it. If they fell Obliquely, as AB and DC; the Angles of Incidence and »; and confequently, alfo the Angles of Inclination x and/, will be equal. But the Sines of the Angles of Inclination x and y, have the fame Ratio to the Sines of the refracled Angles m and »; .therefore the refracl- ed Angles m and n ate alfo equal; confequently the refracled Rays parallel.
Hence a Glafs, plain on both Sides, being turn'd directly to the Sun ; the Light pafling through it will be propagated after the
fame
