Page:Harold Dennis Taylor - A System of Applied Optics.djvu/30

 holds good if we put u for A..Q, r for the radius A..C, and ù for A..q, and this formula interprets itself for all cases, provided the following conventions are strictly adhered to, viz.:—

The radii of all surfaces, whether convex or concave, to be considered intrinsically positive with respect to the conjugate distances whose signs are to be assessed.

Thus, in the case of Fig. 4c, A..Q is convergent and therefore u is negative, and

$\textstyle{ \frac{\mu}{u'} = \frac{\mu -1}{r} - \frac{1}{u} }$

becomes

$\textstyle{ \frac{\mu}{u'} = \frac{\mu -1}{r} + \frac{1}{u} }$

And, again, in a case where Q..A in Fig. 4a becomes less than $$\textstyle{ \frac{r}{\mu - 1} }$$, then of course $$\textstyle{ \frac{\mu}{u'} = \frac{\mu -1}{r} - \frac{1}{u} }$$ gives a negative result, and the refracted pencil is shown to be divergent, as in Fig. 4e.

If the rays of the incident pencil are parallel and therefore

$\textstyle{ \frac{1}{Q..A} = zero }$

therefore