If parallel rays of light, as a b c d e f g, Fig. 6. Plate I. fall directly upon a convex lens A B, they will be so bent, as to unite in a point C behind it. For the ray d D which falls perpendicularly upon the middle of the glass, will go through it without suffering any refraction: but those which go through the sides of the lens, falling obliquely on its surface, will be so bent, as to meet the central ray at C. The further the ray a is from the axis of the lens, the more obliquely it will fall upon it. The rays a b c d e f g will be so refracted, as to meet or be collected in the point C, called the principal focus, whose distance, in a double convex lens, is equal to the radius or semi-diameter of the sphere of the convexity of the lens. All the rays cross the middle ray at C, and then diverge from it to the contrary side, in the same manner as they were before converged.
If another lens, of the same convexity, as A B, Fig. 6. Plate I. be placed in the rays, and at the same distance from the focus, it will refract them, so that after going out of it, they will all be parallel again, and go on in the same manner as they came to the first glass A B, but on the contrary sides of the middle ray.
The rays diverge from any radiant point, as from a principal focus: therefore, if a candle be placed at C, in the focus of the convex lens A B, Fig. 6. Plate I. the rays diverging from it will be so refracted by the lens, that after going out of it, they will become parallel. If the candle be placed nearer the lens than its focal distance, the rays will diverge more or less, as the candle is more or less distant from the focus.
If any object, A B, Fig. 7. Plate I. be placed beyond the focus of the convex lens E F, some of the rays which flow from every point of the object, on the side next the glass, will fall upon it, and after passing through it, they will be converged into as many points on the opposite side of the glass; for the rays a b, which flow from the point A, will converge into _a b_, and meet at C. The rays c d, flowing from the point G, will be converged into _c d_, and meet at g; and the rays which flow from B, will meet each other again at D; and so of the rays which flow from any of the intermediate points: for there will be as many focal points formed, as there are radiant points in the object, and consequently they will depict on a sheet of paper, or any other light-coloured body, placed at D g C, an inverted image of the object. If the object be brought nearer the lens, the picture will be formed further off. If it be placed at the principal focus, the rays will go out parallel, and consequently form no picture behind the glass.