If the object, A P, C, be brought near er to the glass, the picture, a b c, will be removed to a greater distance ; for then, more rays flowing from every single point, will fall more diverging upon the glass; and therefore cannot be sO soon col lected into the corresponding points be hind it. Consequently, if the distance of the object, A B C (fig. 7), be equal to the distance, e B, of the focus of the glass, the rays of each pencil will be so refrac ted by passing through the glass, that they will go out of it parallel to each other; as d e lI, f h, from the point C ; d G, e K, f D, from the point B ; and from the point A; and therefore there will be no picture formed behind the glass.
If the focal distance of the glass, and the distance of the object from the glass, be known, the distance of the picture from the glass may be found by this rule, vi:. multiply the distance of the focus by the distance of the object, and di vide the product by their difference ; the quotient will be the distance of the pic ture.
The picture will be as much bigger, or less, than the object, as its distance from the glass is greater or less than the dis tance. of the object : for (fig. 6) as B e is to eb, so is AC thee; so that if A B C be the object, c b a will be the picture ; or if c b a be the object, A B C will be the picture.
If rays converge before they enter a convex lens, they are collected at a point nearer to the lens than the focus of paral lel rays. If they diverge before they en ter the lens, they are then collected in a point beyond the focus of parallel rays ; unless they proceed from a point on the other side at the same distance with the focus of parallel rays ; in which case they are rendered parallel.
If theyproceed from a point nearer than that, they diverge afterwards, but in a less degree than before they entered the lens.
When parallel rays, as a b cde (fig. 8), pass through a concave lens, as A B, they will diverge after passing through the glass, as it they had come from a radiant point, C, in the centre of the convexity of of the glass ; which point is called the " virtual, or imaginary focus." Thus, the ray, a, after passing through the glass, A II, will go on in the direction, 1, as if it had proceeded from the point, C, and no glass been in the way. 'Fite ray, b, will go on in the direction, m 7i ; the ray, c, in the direction, o p, &c. The ray, C, that falls directly upon the middle of the glass, suffers no refraction in pass ing through it, but goes on in the same rectilinear direction, as if no glass had been in the way.
If the glass had been concave only on one side, and the other side quite flat, the rays would have diverged, after passing through it, as if they had come from a ra.
diant point at double the distance of C from the glass ; that is, as if the radiant had been at the distance of a whole dia meter of the glass's convexity.
If rays come more converging to such a glass, than parallel rays diverge after passing through it, they will continue to converge after passing through it ; but will not meet so soon as if no glass had been in the way; and will incline towards the same side to which they would have diverged, if they had come parallel to the glass.
Of Reflection. When a ray of light falls upon any body, it is reflected, so that the angle of incidence is equal to the angle of reflection ; and this is the fun damental fact upon which all the pro perties of mirrors depend. This has been attempted to be proved upon the principle of the composition and resolu tion of forces or motion : let the motion of the incident ray be expressed by A C (fig. 2); then A D will express the parallel motion, and A B the perpendicular mo tion. The perpendicular motion after re. flection will be equal to that before re flection, and therefore may be express ed by DC = A D. The parallel motion, not being affected by reflection, con tinues uniform, and will be expressed by DM.= AD; therefore the course of the ray will be C M, and by a well-known pro position in Euclid A C D= D C M. The fact may, however, be proved by expe riment in various ways ; the following method will be readily understood.
Having described a semicircle on a smooth board, and from the circumference let fall a perpendicular bisecting the dia meter, on each side of the perpendicular cut off equal parts of the circumference ; draw lines from the points in which those equal parts are cut off to the centre ; place three pins perpendicular to the board, one at each point of section in the circumference, and one at the centre ; and place the board perpendicular to a plane mirror. Then look along one of the pins in the circumference to that in the cen tre, and the other pin in the circumfer ence will appear in the same line produc ed with the first, which spews that the ray which comes from the second pin, is reflected from the mirror at the centre of the eye, in the same angle in which it fell on the mirror. 2. Let a ray of light, passing through a small hole into a dark room, be reflected from a plane mirror, at equal distances from the point of re flection, the incident, and the reflected ray, will be at the same height from the surface.