OF NEWTON'S OPTICS. 



21 



half of I m, and from m' draw m! p' 

 perpendicular to lm' ; the line I p' will 

 be the direction which the ray p I will 

 take in passing through the denser me- 

 dium. 



Now suppose that a ray PI,/#. 23, 

 Fig. 23. 



were to meet I in such a direction that 

 M I is two-thirds of I S. If in this case, 

 in conformity with the rule just ex- 

 plained, we take a length from I equal 

 toIM, together with the half of I M, 

 that length will be I S', and S' would be 

 the point from which the perpendicular 

 (m'p 1 , see last fig.*) should be drawn to 

 meet the circumference. But this point 

 S' being itself on the circumference, the 

 perpendicular (m'p') altogether disap- 

 pears, its length being reduced to abso- 

 lutely nothing ; and the point (p') of 

 the circumference to which the ray is 

 deflected, would be the point S' itself. 

 Thus the Snellian law would shew that, 

 in this case, the ray incident at I would 

 not pass into the rarer medium. Ex- 

 perience, however, proved that, in this 

 case, the ray PI was reflected according 

 to the common law of reflection, in the 

 direction I P', making the angle P' I S 

 equal to I PS. 



If the incident ray made any angle 

 p I m less than P I M, the law of Snel- 

 lius likewise became inapplicable. For, 

 in this case, m I being more than two- 

 thirds of I S, the distance from I taken 

 upon I S would be beyond the point S, 

 and therefore outside the circle, so that 

 the perpendicular could never meet the 

 circle ; and accordingly the refracted 

 ray could have no direction conformable 

 to this law. In all such cases experi- 

 ment shewed that the ray was reflected. 

 In this illustration we have supposed 

 the fixed proportion to be two-thirds, 

 but the conclusion may be drawn if any 

 other proportion be adopted. 



It appears, therefore, that in passing 

 from a denser medium into a rarer there 

 is a certain degree of obliquity beyond 

 which the ray cannot be refracted ; and, 

 on the contrary, will be reflected back 

 into the denser medium, according to 



the common law of reflection. It fur- 

 ther appears, by what has just been ex- 

 plained, that this degree of obliquity, 

 which limits the possibility of refraction, 

 depends on the degree of refraction 

 which the ray suffers in passing from 

 the one medium into the other, and that 

 the limiting obliquity is greater where 

 this refraction is greater. 



Aware of this property of refracting 

 media, Newton perceived, that if the 

 doctrine of unequal refrangibility were 

 granted, it would follow that the limiting 

 obliquity, in passing from a denser me- 

 dium to a rarer, would vary with the 

 refrangibility of the light, being greater 

 for the violet and more refrangible lights 

 than for the red and less refrangible 

 lights. Thus it would follow that those 

 lights which had a greater aptitude for 

 refraction, were also more susceptible 

 of reflexion, and vice versa. He ac- 

 cordingly submitted the doctrine to this 

 test by the following ingenious experi- 

 ment. 



(32.) He took two prisms, B A V,fig. 

 24, and C DB, of the same quality of 



Fig. 24. 



vibgyor 



glass, having the angles A and D right, 

 and the angles at B and C, in each 45, 

 and placing their broadest faces B C to- 

 gether, tied them in this position, so as 

 to form a square prism. This compound 

 prism was placed before an aperture F, 

 which admitted a beam F M of the sun's 

 light, so as to fall perpendicularly on the 

 face AB of the prism. This ray was 

 incident upon the thin plate of air B C 

 between the prisms, which were not 

 brought into absolute contact. Passing 

 through this and the second prism, it 



