82 



OF OPTICAL INSTRUMENTS. 



and — — , or -— _— — -jr' — r'jrj 



—4 — j,':r', 3r'jr'=:4 — r', and the square of the sine of in- 

 cidence DEB, r'x»=^ (4— r'). The whole angle of devia- 

 tion in a sphere of water, is thus found to be for red rays, 

 42°, and for violet 40i° ; so that the external part of the 

 rainbow is red. When there are two intermediate reflec- 

 tions, we have for the ultimate inclination, first the devia- 

 tion at the first surface, then at each 

 reflection two right angles, lessened 

 by twice the angle of refraction, and 

 again, the deviation at the transmis- 

 »ion ; so that the four right angles ^^■- 



destroying one another, the whole incliirattSn is twice the 

 difference of the angle of deviation, and twice the angle of 

 refraction, and the tangent of the angle of incidence must 

 be three limes the tangent of the angle of refraction ; 

 whence we have r'i*=J (9 — »'). The whole deviation of 

 red rays, twice reflected, is about 51°, and of violet rays, 

 54° ; so that in this rainbow the violet colour is external. 



464. Theorem. In the e^'e of an animal, 

 the image which is formed on the retina is 

 inverted with respect to the object. 



The eye is an irregular spheroid, composed of transparent 

 substances of various refractive densities, calculated to col- 

 lect the rays of light, diverging from each point of an ob- 



ject, on a distinct point of its posterior concave surface, 

 according to the angular place of the object. The first re- 

 fraction is at the surface of the cornea ; but the cornea, 

 being very nearly of equable thickness, has little effect by 

 its own refractive power. Its concavity is filled and dis- 

 tended by the aqueous humour, which is partially divided 

 by the uvea or iris, perforated by the pupil. Immediately 

 behind the uvea, and connected to its base by the ciliary 

 processes, isfhe crystalline lens, a substance much more 

 refracdjse^an the aqueous humour, and increasing in den- 

 sity^wards its centre. The remaining cavity is filled by 

 an aqueous fluid, lodged in a texture of extremely fine 

 membrane, and called the vitreous humour. The retina 

 which is capable of transmitting to the sensorium the im- 

 pression of the colour and intensity of the light, together 

 with a distinction of the precise situation of the focal point, 

 lines the whole posterior part of this cavity, it is semitranx- 

 parent, and supported by the choroid, a very opaque black 

 or brown membrane, continued from the uvea and ciliary 

 processes ; but immediately where the retina is connected 

 with the optic nerve, the choroid is necessarily perforated; 

 and at this part a small portion of the retina is insensible^ 

 The whole is surrounded by an opaque continuation of the 

 cornea, called the sclerotica. 



An image is formed on the retina according to the com- 

 mon laws of refraction, it is therefore inverted with respect 

 to the object ; but this inversion has no relation to the trans- 

 mission of impressions constituting vision. 



4()5. Theorem. If a sphere, of which 

 the radius is a, have a nucleus of uniform 

 density, its radius being b, and its refractive 

 density to that of the surrounding medium 

 as r to 1, and if the external parts of the 

 sphere vary in density according to a certain 

 power of the distance from the centre, until 

 they become at the surface similar to the 

 surrounding medium, the distance of the 

 principal focus of the sphere from the centre 



. 9-H rab l.r 

 will be—- — .— ,qbems— ; and 



if a lens consist of two equal portions of such 

 a sphere, the principal focal length of the 

 lens will be less by one fourth of the thick- 

 ness of the portion removed. 



Since the density varies as a certain power j of the dis- 



1,1 / ^\1 



tance, 1 : r :: a : b , and rl=f — ) , whence 9=log. r : 



i l.r 



log. — , or J ^_^^ . Now let AB be the path of the 



