General and practical optics / by Lionel Laurance.

  • Laurance, Lionel.
Date:
1914
Catalogue details

Licence: In copyright

Credit: General and practical optics / by Lionel Laurance. Source: Wellcome Collection.

Provider: This material has been provided by UCL Library Services. The original may be consulted at UCL (University College London)

    163/390 (page 153)
    CHAPTER XIII OBLIQUE CYLINDRICALS AND OBLIQUE SPHERIGALS Powers of a Single Cyl.—If a lens measure be placed in contact with the maximum meridian M. of a cyl. (Fig. 138) we obtain the highest possible curvature from that cylindrical. Along the axis the instrument would indi- cate 0, and between these two the recorded power w^ould vary. Suppose the two fixed legs touch at d d, then the sag, of the central leg indicates the power which is based on the formula r = d/2 S (vide The Spherometer), and the curvature c = 2 S/d^, where d is half the distance d d. If the sag were a fixed quantity c varies inversely with d- Let the instrument be turned so that the legs lie on the meridian at an angle b with M; then f//cos h^d-^. If now the sag were the same as before it is because the distance between the legs is greater, curvature at bearing to the curvature c at M the relationship gJc = d'^/d^^, where d^ is the new distance d^ between the / ( A/, Fig. 138. central and one of the fixed legs in the meridian M^. But d-^^djm^ b, so that c, d:^ d'^ cos- b « ? c ^^1- d^ or Cj^ = c cos^ b Now the dioptric powers D at M, and D^^ at are directly proportional to the curvatures c and Cj^ respectively, so that in the meridian AI^ the power of the lens Dj^ = D cos^ b, or what is the same, Dj = D sin- a where a is the angle between ikfj and the axis. Similarly it can be shown that in the meridian at right angles to the power = D sin- b, or D cos- a. If we consider the angle a between a given meridian and the axis of a cyl., the power varies as sin''^ a; if we consider the angle b between it and the maxi- mum meridian, the power varies as cos^ b.