A System of Optics; A Treatise on the Reflexion and Refraction of Light (Paperback)

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 edition. Excerpt: .../' g The single equivalent lens must have a focal-l, and therefore the best possible form would give y 227 4 y 65 y Example 3. Let four lenses be disposed as in Fig. 92, the focal lengths being as 3, 4, 4, 3, and the intervals 4, 6, and 5y: the original inclination of the pencil to their common axis being very small. Consequently the least value of Q--would have been 0,3 yx2. J 123. We have yet to investigate the case of a pencil passing through two or more lenses under the condition that the place at which its axis intersects that of the lenses after its final emergence is invariable. Supposing at first that there are but two lenses, it is easy to see that the second is exactly in the predicament of the single lens in Art. 100, so that But at the first lens, c1 is variable, because bs is so, and bt is variable on two accounts, namely, the variation of ct and the aberration of the first lens. We have, therefore, -L =-i-i + i + s lil b, /. ft?T '8/, - Again, J Jj. u 2 D 2 2-2 D #2 Example. Instead of the single lens in the Example at p. 131. let there be employed two lenses such as those described in Example 2. p. 157. 124. Prop. 30. To determine the form of a pencil after passing eccentrically through several lenses. In Proposition 22, we found for a single lens the following results, 11 1 if 1) 2 i _ i i if i) # Kf l+7l +-v' In passing to a second lens, we must observe that k will, like b in the last Proposition, be subject to the variation of y, and that there must be introduced into the equations, the term + dh. Now dh2=--dki, and the equations show that as the last i o1 T. 1 l terms are the variations of-, -, and contain--, --as factors Now, in a small term, we may assume--=-, for in the former Proposition it was argued that...