306 



THE POPULAR EDUCATOR. 



black paint, and after drawing a perpendicular line, A A, and a 

 horizontal one, which will be the diameter of the circle, imagine 

 the horizontal line to represent the surface of the water, and the 

 other will of course be perpendicular to it. Let B c be the incident 

 ray, and c D the refracted ray ; if a dotted line is drawn from 

 the extremity of the arc at B to the diameter A, that will be the 

 sine of the angle of incidence, and the other dotted line, drawn 

 from the extremity of the arc at D to the diameter A, will be 

 the sine of the angle of refraction ; then if the sine of the angle 

 of incidence, which may be supposed to be four inches, is 

 livided by the sine of the angle of refraction, ascertained by 

 direct experiment to be three inches, the quotient will be 

 1'333, which is called the index of refraction for water. If the 

 lines are drawn upon the plate with black varnish, the plate 

 can be held upright in water, and the young student may trace 

 out and study more practically that which might otherwise 

 puzzle him. 



There are particular positions, as when light passes from a 

 dense into a rare medium viz., from glass into air in which 

 the refracted ray becomes parallel with the surfaces of the glass 

 and air. At a more oblique angle, when light passes through 

 the denser medium, and becomes incident upon the surfaces of 

 the glass and air, the ray is no longer refracted, but undergoes 

 total reflection. This fact is well illustrated by placing an 

 engraving, E E, behind a prism, p, placed as in Fig. 5. 



The prism and picture should face the window, and if they 

 are placed on a stand level with the eyes, it is curious to notice, 

 as the spectator walks round, that there are certain very 

 oblique positions at the sides, A A, where the light from the 

 window only is reflected and no picture is visible, and where 

 the reflecting surface shines like silver, because total reflection 

 occurs ; but as the observer moves round in a half circle, say 

 from B to B, the picture reappears, and again disappears as he 

 passes to the opposite sid3, and looks very obliquely at the 

 surface behind which the picture is placed. The brilliancy of 

 the diamond is greatly owing to the total reflection of light, 

 which becomes visible at smaller angles of incidence in conse- 

 quence of the very high refractive power of this, the purest 

 natural form of carbon. 



A lens, in dioptrics (from Hioirrpov, a perspective instrument), 

 is defined by an old author to signify a small roundish glass of 

 the figure of a lentil, which, in scientific botany, is called the 

 lens ; and this Latin word is said to have originated from lenis 

 (mild), because those who fed upon this sort of pulse were sup- 

 posed to become mild and gentle in disposition. There are two 

 great classes of lenses, called convergent and divergent lenses. 

 If the properties of concave and convex mirrors are understood, 

 it is easy to remember those of lenses of the like figure, because 

 the latter have exactly opposite properties to the former. 



A double convex lens is a good example of the convergent 

 class : divergent rays become parallel if passed through a lens 

 of this shape, and parallel rays are made so convergent that they 

 meet at a point called the focus, and termed the principal focus. 

 The rays of light from the sun are nearly parallel, and hence 

 "the principal focus," or jire-place, of a double convex lens 

 corresponds with that spot where the greatest heat is accumu- 

 lated, as in a burning glass, so that a double convex lens is a 

 simple form of burning glass. 



In the illustration (Fig. 6) the divergent rays passing from an 

 aperture, E, in tha copper chimney of an argand oil or. gas light, 

 fall upon a double convex lens, A A, and by refraction become 

 parallel, and fall upon the screen of paper, s ; by reversing the 

 description, and starting from s, as the source of parallel rays, 

 they are collected by A A, and meet at the focus, or fire-place, E. 

 A double concave lens (Fig. 7) is a good example of the 

 divergent class. Rays of light already divergent become still 

 more so if allowed to fall upon a lens of this form. Parallel 

 rays are made divergent, and even convergent rays are turned 

 in the opposite direction, and made less so by a double con- 

 cave lens. 



With two prisms the principle of the double convex or con- 

 cave lens is demonstrated in the most instructive manner. By 

 placing the prisms base to base, and passing a pencil of sun- 

 Jight from a hole in a shutter through them, the rays are bent 

 inwards, and converge to a point, as they would do with a 

 convex lens, and this is easily seen by referring to Fig. 8. 



When the position is reversed, as in Fig. 9. and the prisms 

 are held edge to edge, they virtually form a double concavo 



lens, and the same rays are now scattered outward, and be- 

 come divergent. 



Lenses have various figures, and the lines that bound then 

 may be portions of circles or ellipses, or they may be right 

 lines. Generally speaking, one or both sides are portions of a 

 spherical surface, or one side may be a portion of a sphere, and 

 the other a plane surface. Thus there are plano-convex or 

 plano-concave lenses, one side of which would be flat, and the 

 other curved; or concavo-convex lenses, concave on one side 

 and convex on the other, and if the concavity exceeds the con- 

 vexity, it would be regarded as a concave lens belonging to the 

 divergent class. A most useful lens is the meniscus, meaning 

 a little moon or crescent, one of whose surfaces is convex and 

 the other concave ; but as the convexity exceeds the concavity, 

 this would be considered to be a convex lens, and must be 

 classed with the convergent lenses. 



Before there were such facilities for obtaining glass lenses of 

 almost any size or shape, it was always thought necessary to 

 give a description of the mode of grinding and polishing lenses 

 in works on optics ; .and as many of our younger readers may 

 have lathes, and would like to be able to say that they had 

 constructed a simple telescope, and ground their own lenses, 

 the following particulars, published many years ago, will be 

 found to be eminently practical, and capable of giving fa 

 results : 



" Manner of Grinding Lenses. A little piece of copper 

 cemented to the end of the arbor of a lathe, and turned til 

 it forms a dish or bason of the diameter of the lens required 

 Then a piece of clear glass is cemented, on one side of 

 flat sides, to the end of a little mandrel, with black Spanisfc 

 wax ; and thus ground, on the side not cemented, on a grind- 

 stone with water, till it hath nearly acquired a convex figure. 

 It is finished in the lathe by turning it in the basin with fino 

 wot sand, grit stone, or emery. The grit must be often repeated 

 fresh till the lens appear very round ; when it comes to that 

 point they cease to take any fresh grit stone, but continue to 

 turn it in the basin, till the remains of the sand are become so 

 fine as to have polished it. This they perceive when, upon 

 wiping it, the image of the window of the place is seen 

 painted on its surface ; if it does not, it is rubbed in water 

 without any sand, and turned till it hath got a polish. The 

 basin is then covered, withinside, with two or three folds of 

 linen, and the polish finished with putty powder, or tripoli of 

 Venice steeped in water. It is known to be perfectly polished 

 when, viewing it with a magnifier, there appear no scratches 

 of the sand. The cement is then broken off, and the side 

 polished cemented, to work and grind the other, as before, till 

 the edges of the lens become sharp, and it be perfectly polished 

 on either side. When finished, it is washed in spirits of wine, 

 to take off all remains of the wax." 



According to the mode now generally practised, optica 

 glasses are fixed on blocks by means of a cement, and grounc 

 with emery on a tool of proper convexity or concavity ; if thej 

 are small, a large number is fixed on the blocks at the samo 

 time. The tool is sometimes first turned round its axis by 

 machinery, and when the lenses are to be finished, a compound 

 motion is given to it by means of a crank; and in order to 

 make it work smooth, the wheels turn each other by brushes, 

 instead of cogs. The point of the lens where its two surfaces 

 are parallel is determined by looking through it at a minute 

 object while it is fixed in a wheel with a tubular axis, and shift- 

 ing it until the object appears no longer to move ; a circle is 

 then described as it revolves, in order to mark its outline. 



The dishes in which lenses are ground are of bell metal, and 

 the emery is prepared by elutriation. The writer has seen five 

 hundred spectacle-glasses ground and polished at the same 

 time by machinery at Sheffield, the operation being principally 

 conducted by women, who exhibited the greatest dexterity in all 

 the manipulations, such as cementing the glasses on to the 

 tool, and adjusting the basins and emery-powder to the work 

 required to be done. 



The focal length of any convex lens is easily found, by hold- 

 ing its axis in a line with the sun ; the burning-point, or the 

 place where the rays are concentrated to the smallest speck, is 

 its focus ; the distance of that focus from the lens is its focal 

 length. 



The nearer an object is brought to the focus of a convex lens 

 the larger will be the image. The brightness of an image 



