Page:Optics.djvu/84

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The following therefore are corresponding values,

∆	=	∞,	r/m−1,	0,	−r,	∞
∆′	=	−mr/m−1,	∞,	0,	−r,	mr/m−1.

Cases 3 and 4 have, in fact, been discussed in the two others, we will therefore only exhibit the principal corresponding values of ∆ and ∆′.

Case 3.	∆	=	∞,	mr/m−1,	r,	0,	∞,
	∆′	=	−r/m−1,	−∞,	r,	0,	−r/m−1.
Case 4.	∆	=	∞,	0,	−r,	−mr/m−1,	∞,
	∆′	=	r/m−1,	0,	−r,	∞,	r/m−1.

Upon the whole we may collect the following results.

In Case 1, divergency is given to incident rays, except when they proceed from a point between the centre and the surface.

In Case 2, convergency is given.

In Case 3, convergency, except when the focus of incident rays is between the centre and surface.

In Case 4, divergency in all cases.

Of course we except the case of rays proceeding from, or to the centre of a surface, which are not refracted at all.

85. We now pass on to a more useful part of this subject, which treats of Lenses, that is, of refracting media terminated by two spherical surfaces.

There are several kinds of these:

1. The double convex, of which Fig. 80. represents a section through the axis.