416 



LIMITS OF OPTICiL CAPACITY OF THE MICROSCOPE. 



angles to the axis, and from which rays pass through the system. 

 The angle formed between any one of such ra^^s and the axis, we 

 shall call the divergence-angle of that particular ray. Any plane 

 supposed to extend through the axis and along the ray, constitutes 

 the incidence plane of that ray at the first refraction and will 

 include, therefore, the same ray after its next refraction, and con- 

 sequently after every subsequent refraction. Of this plane which 

 will be divided in crossing the axis into two halves, one half will be 

 treated as positive, the other as negative, and in correspondence 

 therewith, the divergence-angle of the ray as positive or negative, 

 according as the ray proceeds towards the positive or negative 

 half of the plane. These postulates being settled the rule may be 

 thus stated : — 



Theorem. 



In a centred system of spherical refracting or reflecting surfaces the 

 product of the divergence-ayigle of any ray^ the refraction index of the 

 medium through which that ray passes ^ and the magnitude of the image 

 to ivhich the rays passing through that medium lelong, remains un- 

 changed hy every refraction, provided always that the conditions of 

 production of an accurate image are duly preserved. This product 

 will therefore have the same value after emergence of the rays as it had 

 before they entered the system of lenses. 



Let « J be the axis of a lens system. 



— ]^ U one of the refracting surfaces. 



— c the centre of its curve. 



