Again, the quantity discharged in the time dt is which being substituted in (1) gives the quantity of air expelled OPTICS. 768. If q, q', denote the distances of the object and its image from the centre of the reflector whose radius is r, we have (see Coddington's Optics, p. 8) Also, when the object, 0, is very small, compared with the radius of the reflector, it and its image o' may be considered circular arcs, and in the limit, we have get rq r+ 2q ::r + 2q: r. But, if 0, 'be the angles subtended by 0, 0' at the vertex, we 769. If A,'A" denote the distances of the object o and image o' from the lens; then (Coddington's Optics, p. 120) F being the distance of the principal focus .. 0:0′ :: A: FA :: A+F: F. Now, by the question, 0:0' :: 1: 2, and since the image is to be erect, the object and image are on the same side of the lens, and the distance of the principal focus on the other side is negative .. 1 : 2 :: F-A:F A= When rr 770. F m- 1 r+r' 2 X rr' The principal focal length, measured from the centre 771. eye, and Let a be the distance between the object and the the distance of the lens from the object; then (Cod 772. Since the angle of deviation increases with the angle (p) of incidence, (see Wood's Optics, p. 46,) the rod will be most bent, when this latter angle is a maximum. Now, the angle of refraction being 90°, is a maximum, and then 773. Let r be the radius of the base, and h the height of the cylinder. Then, if p, q' be the angles of incidence and refraction, we have 774. The density of the sun's rays, or the brightness of his image when viewed with a reflector or refractor oc area of aperture × power: (see Wood, p. 120.) Hence, supposing the power the same in both the reflector and lens we have, by the question 2r, 2r being the linear apertures, and F, F' the focal lengths. But F2F (Wood, pp. 20, 95.) 2 775. Since the object 0 is very small, it may be considered an arc of a circle concentric with a vertical section of the cylinder. Hence the image o' will also be a circular arc concentric with the object, and if q, q' denote their radii, we have which gives the magnitude of the image, when q and ƒ are known. 776. In the sphere the angle of incidence at the second surface is always equal to the angle of refraction at the first surface. Hence it will readily appear, upon drawing the figure, that the angle of incidence at the first surface is equal to the angle of refraction at the second, and therefore the ray intercepted between the surfaces will be the base of two opposite isosceles ▲, whose vertices are at the centre and intersection of the first and last directions of the ray. Now, when the distance of the centre from this radiant chord is given, the chord itself is given, and the |