Manual of optics, by J.A. Galbraith and S. Haughton

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Page 19 - When a ray of light passes from one medium to another, it is refracted so that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities in the two media.
Page 11 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 23 - ... that the ratio of the sines of the angles of incidence and refraction is constant for refraction in the same medium, was effected by Snell and Descartes.
Page 12 - In either case prove that the focal length of the mirror is a mean proportional between the distances of the conjugate foci from the principal focus.
Page 42 - A the divergence of the pencils proceeding from it will exceed the divergence of rays proceeding from the focus; and therefore the effect of the lens will only be to diminish this divergence, and make the rays appear to proceed from an image mn farther away from the lens than the object, and at the same side. It...
Page 8 - Q from the mirror, the distance of q from the mirror, and the radius of the mirror) ; any two of which being given, the third can easily be found.
Page 39 - Q,0q be the path of a ray incident upon and refracted by any thin lens, convex or concave. Let C be the centre of the lens, and let a circle be described, with C as centre, and radius equal the focal length of the lens.
Page 15 - Hence we may conclude that the image of a body seen in a convex mirror is always behind the mirror, and less than the object in the ratio of mn : MN, ie in the ratio of C : NC, the distances of the image and object from the centre of the mirror.
Page 16 - M of the object, and, after reflexion, converges to the conjugate focus m, and thence diverges again to fall upon the eye at E. It is evident that the image mn is inverted, and smaller than the object, in the ratio of nC : NO.
Page 78 - Newtonian, with the same object speculum of 4 feet focal length, and the same eye-piece ; the secondary mirror of the Cassegrainian telescope having a focal length of 4 inches.

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