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. 1829 Excerpt: ...and is sometimes used for the same purposes. We will, therefore, examine the modifications which a pencil of rays will experience in passing through it. It was observed (Art. 69.) that there are three different ways in which the axis of a pencil might pass through a lens: (1) Directly through the center. (2) Obliquely ...
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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. 1829 Excerpt: ...and is sometimes used for the same purposes. We will, therefore, examine the modifications which a pencil of rays will experience in passing through it. It was observed (Art. 69.) that there are three different ways in which the axis of a pencil might pass through a lens: (1) Directly through the center. (2) Obliquely through the center. (S) Excentrically, Now, in a sphere, it will easily be seen that the second Case is merged in the first, the points C, D, and E, of the lens all coinciding with O, the center. The third Case will be found to have this peculiarity, that the angles of incidence and emergence are necessarily equal. 106. Prop. 24. A small pencil of rays passes through the center of a sphere: required the position of the focus. Case 1. Parallel Rays. Let QAB (Fig. 83.) be the axis of the pencil, QR a second ray, refracted into the directions RS, SF. Produce QR, FS to meet in L. Join OR, OS. Produce RS to cut AB in Q'. Then the angles of refraction ORS, OSR are equal to one another, therefore the angles of incidence and emergence ORL, OSL are also equal... /L LSR = /.LRS, .-. L FSQ'-tSQ'F;.: SF = FQ'. 3 3 For instance, if u =-, OF =-r. 2' 2 The principal focus is, therefore, at the distance of a radius and a half from the center. If M = 2 OF=r, or the point F coincides with B. If fx 2, F is between O and Z?. 107. Case 2. Divebging Bays. Let QJ5 (Fig. 84.) be the axis of the pencil, QRSq a second ray, determining the focus by its ultimate intersection with the axis. - As in Proposition 11. we have, at the first refraction, QO QO QR ' Q'R " M: ' and, therefore, for the first approximation, QO QO QA: WA." h QA_10JA r Q0- QO' q fxp V A so that, combining the equations (l) and (2), We have, therefore, measuring the distances from t...
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Add this copy of A Treatise on the Reflection and Refraction of Light: to cart. $61.07, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2015 by Palala Press.