75 
Dr Brewster on Single Microscopes. 
As the incidence of the rays upon AC is very little different 
from 45° when ABC is a hemisphere, and when the apertures 
are small, they will always be reflected at a greater angle than 
that at which total reflexion takes place and therefore no light 
will be lost at the reflecting surface. It is obvious, therefore, 
that by this method of using the lens ABC, we have produced 
the same effect as if we had added another hemispherical lens 
like AB'C, or employed the whole sphere ABCB', from which 
the rays would have emerged at d', e\f after refraction, in the 
very same manner as at d, ^ 5 /after reflexion. As it is impos- 
sible to grind a spherical glass sufficiently accurate for optical 
purposes, the Reflecting or Catoptiic Lens ABC should be com- 
pared with a double convex lens, equal to the plano-convex 
lenses AB and BC put together. Now, in constructing such a 
lens, we are liable to the error arising from bad centering, in con- 
sequence of the two convex surfaces being ground and polished 
in succession ; but in the reflecting lens this source of error is 
entirely removed, because the two refracting surfaces, AB and 
BC, are ground simultaneously in the same tool. 
As the corners at A and C are not necessary to the operation 
of the lens, a complete hemispherical surface of 180° will not 
be required. An arch from 120° to 140° will be sufficient for 
every purpose, and hence it will be easy to employ the perisco- 
pic principle, which we shall presently have occasion to de- 
scribe. We have only to remove the polish from an annular 
space of the polished surface A C, having Ac or Ca for its 
breadth, in order to exclude the lateral or obliquely incident 
rays. 
The reflecting lens ABC may be considered as composed of a 
right-angled prism ABC, and of two plano-convex lenses, AB 
and BC, and will therefore form a new diagonal eye-piece^ (fl 
the most perfect construction. Opticians have frequently ground 
one face of the rectangular prism into a convex surface ; but, in 
so far as I can learn, they have never attempted to form the 
whole eye-piece out of a hemispherical lens. The simplicity of 
* The sine of the angle of total reflexion being equal to - — ^ — will 
index of refraction, 
be about 4-1* in crown glass. 
