ON THE GENERAL LAWS OF OPTICAL INSTRUMENTS. 279 



When d = 0, all these values become infinite, and the compound instrument 

 becomes a telescope. 



PROP. VII. To find the linear magnifying power, the elongation, and the 

 centre of the instrument, when the combination becomes a telescope. 



Here (fig. 6) the second principal focus of the first instrument coincides at F 

 with the first of the second. (In the figure, the focal distances of both instru- 

 ments are taken in the opposite direction from that formerly assumed. They are 

 therefore to be regarded as negative.) 



In the first place, F,' is conjugate to F lt for a pencil whose focus before 

 incidence is F l will be parallel to the axis between the instruments, and will 

 converge to F{ after emergence. 



Also if G& be an object in the first principal plane, G.^ will be its first 

 image, equal to itself, and if Hh be its final image 



,TT_ FG' . G,'F t ' 



f~ > 

 /, 



Now the linear magnifying power is - , , and the elongation is - 



because F t ' and H are the images of F l and G^ respectively ; therefore 



/=-, and n=r. 



J* A/2 



The angular magnifying power = m = - = 4^ . 



The centre of the telescope is at the point C, such that 



When n becomes 1 the telescope has no centre. The effect of the instrument 

 is then simply to alter the position of an object by a certain distance measured 

 along the axis, as in the case of refraction through a plate of glass bounded by 

 parallel planes. In certain cases this constant distance itself disappears, as in 

 the case of a combination of three convex lenses of which the focal lengths are 



