OPTICS. 



perpendicular to P ; cut ofFD T and C I 

 equal to three-fourths D A; through T I, 

 draw T I S, cutting- the circumference in 

 8 ; N S drawn from S, perpendicularly 

 upon O P, will he equal to D T, or three- 

 fourths of DA. Then if pins be stuck 

 perpendicularly at A, C, and S, and the 

 board be dipped in the water as far us the 

 line H K, the pin at S will appear in the 

 same line with the pins at A and C. This 

 shews, that the ray which comes from the 

 pin S is so refracted at C, as to come to 

 the eye along the line C A ; whence the 

 sine of incidence A D is to the sine of re- 

 fraction N S, as 4 to 3. If other pins 

 were fixed along C S, they would all ap- 

 pear in A C produced ; which shews that 

 the ray is bent at the suiface only. The 

 same may be shewn, at different inclina- 

 tions of the incident ray, by means of a 

 moveable rod turning upon the centre C, 

 which always keep the ratio of the sines 

 A D, N S, as 4 to 3. Also the sun's sha- 

 dow, coinciding with A C, may be shewn 

 to be refracted in the same manner. 

 The image L, of a small object S, plac- 

 ed under water, is one-fourth nearer 

 the surface than the object. And hence 

 the bottom of a pond, river, &.c. is one- 

 third deeper than it appears to a specta- 

 tor. 



To prove the refraction of light in a 

 different way, take an upright empty 

 vessel into a dark room ; make a small 

 hole in the window-shutter, so that a beam 

 of light may fall upon the bottom at a 

 (fig. 4) where you may make a mark. 

 Then fill the bason with water, without 

 moving it out of its place, and you will 

 see that the ray, instead of falling upon a, 

 will fall at b. If a piece of looking-glass 

 be laid in the bottom of the vessel, the 

 light will be reflected from it, and will be 

 observed to suffer the same refraction as 

 in coming in; only in a contrary direc- 

 tion. If the water be made a little mud- 

 dy, by putting into it a few drops of milk, 

 and if the room be filled with dust, the 

 rays will be rendered much more visi- 

 ble. The same may be proved by ano- 

 ther experiment. Put a piece of money 

 into the bason when empty, and walk 

 back till you have just lost sight of the 

 money, which will be hidden by the edge 

 of the bason. Then pour water into the 

 bason, and you will see the money distinct- 

 ly, though you look at it exactly from the 

 same spot as before. See (fig. 2) where 

 the piece of money at S will appear at 

 L. Hence also the straight oar, when 

 partly immersed in water, will appear 

 bent, *s ACS. 



If the rays of light fall upon a piece 

 of flat glass, they are refracted into a 

 direction nearer to the perpendicular, 

 as described above, while they pass 

 through the glass; but after coming 

 again into air, they are refracted as 

 much in the contrary direction ; so that 

 they move exactly parallel lo what they 

 did before entering the glass. But, on 

 account of the thinness of the glass, this 

 deviation is generally overlooked, and it 

 is considered as passing directly through 

 the glass. 



If parallel rays, ab (fig. 1) full upon a 

 piano convex 'lens, c d, they will be so 

 refracted, as to unite in a point, c, be- 

 hind it; and this point is called the 

 " principal focus," or the " focus of pa- 

 rallel rays;" the distance of which from 

 the middle of the glass, is called the 

 " focal distance," which is equal to twice 

 the radius of the sphere, of which the 

 lens is a portion. 



When parallel rays, as A B (fig. 5) 

 fall upon a double convex lens, they 

 will be refracted, so as to meet in a 

 focus, whose distance is equal to the ra- 

 dius or semi-diameter of the sphere of the 

 lens. 



Ex. 1 . Let the rays of the sun pass 

 through a convex lens into a dark room, 

 and fall upon a sheet of white paper 

 placed at the distance of the principal 

 focus from the lens. 2. The rays of a 

 candle in a room from which all exter- 

 nal light is excluded^ passing through a 

 convex lens, will form an image on white 

 paper. 



But if a lens be more convex on one 

 side than on the other, the rule for find- 

 ing the focal distance is this : as the sum 

 of the semi-diameters of both convexities 

 is to the semi-diameter of either, so is 

 double the semi-diameter of the other to 

 the distance of the focus ; or divide the 

 double product of the radii by their 

 sums, and the quotient will be the dis- 

 tance sought. 



Since all the rays of the sun whicu 

 pass through a convex glass are collected 

 together in its focus, the force of all their 

 heat is collected into that part ; and is in 

 proportion to the common heat of the 

 sun, as the area of glass is to the area of 

 the focus. Hence we see the reason why 

 a convex glass causes the sun's rays to 

 burn after passing through it. See Buns- 

 ING glass. 



All those rays cross the middle ray in 

 the focus f, and then diverge from it to 

 the contrary sides, in the same manner as 

 they converged in cooling 1 to it. If ano- 



