Page:Harold Dennis Taylor - A System of Applied Optics.djvu/32

 or $\textstyle{ \frac{1}{v}=(\mu-1)\left(\frac{1}{r}+\frac{1}{s}\right) - \frac{1}{u'} }$III. which well-known formula applies to all thin lenses whatsoever under the following conventions.

Collective Lenses

The focal length of a collective lens must be considered a positive quantity with respect to the conjugate focal distances. The radii of all convex surfaces are considered intrinsically positive, while the radii of all concave surfaces are considered intrinsically negative, their radii, of course, being always numerically greater than the radii of the convex surfaces in the same lenses, so that the deeper curved surface determines the character of the lens.

If rays of incident pencil are diverging, u is real and +. Figs. 6a and 6e.

If rays of incident pencil are converging, u is virtual and -. Fig. 6c.

If rays of emergent pencil are converging, v is real and +. Figs. 6a and 6c.

If rays of emergent pencil are diverging, v is virtual and -. Fig. 6e.

Dispersive Lenses

The focal length of a dispersive lens is also to be considered a positive quantity with respect to the conjugate focal distances. The radii of all concave surfaces are considered intrinsically positive, while the radii of all convex surfaces are considered intrinsically negative, their radii, of course, being always numerically greater than the radii of the concave surfaces in the same lenses, the deeper curved surface again determining the character of the lens.

If rays of incident pencil are converging, u is virtual and +. Figs. 6b and 6f.

If rays of incident pencil are diverging, u is real and -. Fig. 6d.

If rays of emergent pencil are diverging, v is virtual and +. Figs. 6b and 6d.

If rays of emergent pencil are converging, v is real and -. Figs 6f.

Figs. 6a, b, c, d, e, and f are illustrations of these conventions. As in Fig. 4, and generally throughout this book, all intrinsically positive distances are drawn in full lines, drawn thinner where