16 
METHODS OP PETROGRAPHIC-MICROSCOPIC RESEARCH. 
tured by it in M". This process repeats itself for each new refracting sur- 
face, but in every case a point in the object is pictured as a point in the 
image, with the result that a point of the original object is pictured as a 
FIG. 4. 
point in the final image and a small surface element normal to the axis is 
pictured as a small surface element normal to the axis in the final image. 
For this entire system the equation (5) can therefore be written 
y' . n' . tan u' = y . n . tan u 
(50 
where n and n' are the refractive indices of the original object space and the 
final image space respectively. 
FIG. 5. 
If in a lens system L (Fig. 5), two pairs of conjugate planes M\ and M'\, 
i and M'z be given and also the lateral magnification for each pair 
ft = ^ and /3 2 = 2- s 
the behavior of the system for any ray or point can be readily found. 
Thus any entering ray IP\P* must pass on emergence through the points P'\ 
and P'j of the conjugate planes M'\, M's, and these points suffice to fix its 
direction ; from these relations the fundamental lens formulae can be easily 
derived. In Fig. 6, let a ray PiPj be incident parallel with the axis; then, 
for this ray, 
, and for the emergent ray 5r" J similarly, let the 
y Ps 
Vi js 
incident ray QiQ* emerge parallel with the axis; then y\ = y' s = h' and =^; 
yi Pi 
from the figure it is evident that 
