Page:Optics.djvu/99

 100.Some writers treat of another aberration arising from that which we have been investigating: it is the distance $$qz,$$ (Fig. 97.) $$Aq$$ being the ultimate focal distance and $$qz$$ perpendicular to $$Aq.$$

This distance $$qz$$ is called the lateral aberration, $$qo$$ the longitudinal,

Since $$qv$$ varies as the square of $$AR,$$ it appears that $$qz$$ varies as its cube.

101.It is important, particularly when a lens is used as a burning-glass to determine whereabouts all the refracted rays are collected within the least space, that is, technically speaking, to find the least circle of aberration or diffusion.

Let $$ST$$ (Fig. 98.) be the extreme refracted ray on one side: $$ a ray on the other side intersecting with this in $$n, \ nm$$ perpendicular to the axis. Now it is plain that at the maximum state of $$mn$$, if it has one, all the refracted rays on the same samesame [sic] side with $$Sv$$ will pass through it, and passing from the section to the actual lens, the circle having $$mn$$ for its radius will just contain all the rays, so that it will be the circle we seek.

In order to find $$mn$$ we must know the extreme aberration $$qT:$$ let this be called $$a.$$

Since the aberration (longitudinal) varies as the square of the radius of the aperture,

$$mn=Tm.\frac{AR}{AT}=x.\frac{K}{T}; \quad \therefore mn\propto x,$$ and they are at a maximum together. Errata