(3) A rarer medium with a concave surface, Fig. 68.
(4) A rarer medium with a convex surface, Fig. 69.
In all these figures is the incident ray cutting the axis in ; the refracted ray cutting in . is the centre of the surface.
Let ,
Then
76. It is not possible to obtain a general, simple, algebraical expression from this, but if merely the ultimate value of be required, that is, the limit of its value when the angle is diminished sine limite, we may put , for , for [1]; we have then
that is, (Case1, 3.)
↑There is one case in which has but one value, all the rays being refracted accurately so as to meet in a single point ; it is when