ON THE GENERAL LAWS OF OPTICAL INSTRUMENTS. 277 



Let Q 1 a 1 J5 1 be a ray through B lt the emergent ray will be Q^a^B^, and 

 = l.A 



Now 



> A T> 



so that ~n^5 ~A~i^ n > a constant ratio. 



" 



Cor. If a point C be taken on the axis of the instrument so that 



then 



Def. The point C is called the centre of the telescope. 



It appears, therefore, that the image of an object in a telescope has its 

 dimensions perpendicular to the axis equal to I times the corresponding dimen- 

 sions of the object, and the distance of any part from the plane through C 

 equal to n times the distance of the corresponding part of the object. Of 

 course all longitudinal distances among objects must be multiplied by n to 

 obtain those of their images, and the tangent of the angular magnitude of an 



object as seen from a given point in the axis must be multiplied by to 



it/ 



obtain that of the image of the object as seen from the image of the given 

 point. The quantity - is therefore called the angular magnifying power, and 



71 



is denoted by m. 



PROP. VI. To find the principal foci and principal planes of a combina- 

 tion of two instruments having a common axis. 



Let /, /' (fig. 5) be the two instruments, G^F^ the principal foci and 

 planes of the first, GiF^F^G, those of the second, r^^r, those of the com- 

 bination. Let the ray g^fi^g* pass through both instruments, and let it be 

 parallel to the axis before entering the first instrument. It will therefore pass 

 through F t the second principal focus of the first instrument, and through g t 

 so that 



On emergence from the second instrument it will pass through <j> 3 the 

 focus conjugate to F,, and through g t ' in the second principal plane, so that 



