Humphrey Lloyd Elements of Optics

ISBN 13: 9780217800143

Elements of Optics

9780217800143: Elements of Optics

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1849. Excerpt: ... CHAPTER III. OF LIGHT REFLECTED AT SPHERICAL SURFACES. 27. When a ray of light is incident upon a curved reflecting surface, it is reflected by it in the same manner as by the plane which touches the surface at the point of incidence. Of all curved surfaces the spherical is the simplest. It is also, on account of the comparative facility with which it may be wrought, that chiefly used in the construction of optical instruments. On both accounts it demands the chief consideration. 28. Lemma.--If through any point Q (fig. 8) two lines be drawn to meet the surface of a sphere, one of which, QS, passes through the centre, while the other, QR, is inclined to QS at a small angle, the angle RQS, is to the angle at the centre, RCS, in the inverse ratio of the distances of their vertices from the surface. For, in the triangle QRC,-:--ppo-= Tvo, but the angles RQS, RCS, being small, are as their sines, q. p.; and the point R approaching indefinitely to S, the distances CR and QR are ultimately equal to CS and QS. Hence RQS CS RCS QS' 29. A small pencil of rays being incident perpendicularly upon a concave spherical surface, it is required to find the focus of the reflected pencil. Let RS (fig. 9) be any section of the sphere, formed by a plane passing through the centre, and through Q, the focus of the incident pencil; the line QC, joining these points, is perpendicular to the surface at S, and is, therefore, the axis of the pencil. Let QR be any ray of the incident pencil, meeting the surface at R, and reflected in the direction Rq; and let CR be the radius drawn to the point of incidence. Then, since CR is perpendicular to the tangent plane at the point R, the angles QRC, qRG, are the angles of incidence and reflexion, and are therefore equal. Hence, RqS-RCS = R...

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