SPHERICAL DISTORTION. 



convexity renders a diminished diameter necessary it also pro- 

 duces a diminished focal distance ; and since the aperture 

 (that is, the angle formed by lines drawn from the principal focus 

 to the extremities of a diameter of the lens) increases with the 

 decrease of the focal distance, this decrease may compensate for 

 the decrease of the diameter, so that the aperture may not be 

 diminished. But in fact the decrease of focal distance, much more 

 than compensates for the decrease of the diameter, and in good 

 lenses the aperture is much greater for small lenses of high magni- 

 fying power, than for larger ones with lower magnifying power. 



It is owing to this, that great magnifying powers can be 

 obtained without rendering the illumination of the image 

 injuriously faint, as it would be, unless the aperture of the lens 

 on which it depends were augmented in some degree proportionate 

 to the increase of the power. 



46. SPHEEICAL DISTORTION. 



Independently of the^spherical aberration properly so called, 

 there is another optical effect produced in the image, depending 

 on the form of the lens, which requires notice. 



In the preceding paragraphs it has been assumed that the form 

 of the image is that of the object, and when the image is small 

 this may be considered as practically true. But when the image 

 is considerably amplified the form differs sensibly from that of 

 the object. 



If an object which is straight or flat be presented to a convex 

 lens, outside its principal focus, so that a real image shall be pro- 

 duced on the other side of the lens, the image will not be flat but 

 curved, with its concavity towards the lens. If the object were 

 curved with its convexity towards the lens, its image would be 

 also curved, but with its concavity towards the lens, and the 

 curvature of the image would in that case be greater than that of 

 the object. 



If the object were concave towards the lens, its image would 

 be also concave towards the lens, but with less curvature than 

 the object. 



47. If the curvature of the object be supposed gradually to 

 increase, the concavity still being presented towards the lens, 

 the image will be also concave towards the lens, but its curvature 

 will diminish as that of the object increases, and when the 

 curvature of the object increases to a certain point, the image will 

 become straight or flat. 



If the curvature of the object still continue to increase, the 

 image will become convex towards the lens, and its curvature 

 will increase with that of the object. , 



105 



