CONSTRUCTION OF THE MICROSCOPE. 19 



diverging from that point are rendered parallel. Hence 

 the focus of a double-convex lens will be at just half the 

 distance, or half the length, of the focus of a plano-convex 

 lens having the same curvature on one side. The distance 

 of the focus from the lens will depend as much on the 

 degree of curvature as upon the refracting power (called 

 the index of refraction) of the glass of which it may be 

 formed. A lens of crown-glass will have a longer focus 

 than a similar one of flint-glass ; since the latter has a 

 greater refracting power than the former. For all ordinary- 

 practical purposes, we may consider the principal focus 

 as the focus for parallel rays is termed of a double-convex 

 lens to be at the distance of its radius, that is, in its centre 

 of curvature ; and that of a plano-convex lens to be at the 

 distance of twice its radius, that is, at the other end of the 

 diameter of its sphere of curvature. The converse of all 

 this occurs when divergent rays are made to fall on a 

 convex lens. Rays already converging are brought together 

 at a point nearer than the principal focus : whereas rays 

 diverging from a point within the principal focus are ren- 

 dered still more diverging, though in a diminished degree. 

 Rays diverging from points more distant than the prin- 

 cipal focus on either side, are brought to a focus beyond 

 it ; if the point of divergence be within the circle of curva- 

 ture, the focus of convergence will be beyond it ; and vice 

 versa. The same principles apply equally to a plano- 

 convex lens; allowance being made for the double distance 

 of its principal focus. They also apply to a lens whose 

 surfaces have different curvatures the principal focus of 

 such a lens is found by multiplying the radius of one 

 surface by the radius of the other, and dividing this pro- 

 duct by half the sum of the radii. 



The refracting influence of concave lenses will be pre- 

 cisely the opposite of that of convex. Rays which fall 

 upon them in a parallel direction, will be made to diverge 

 as if from the principal focus, which is here called the 

 negative focus. This will be, for a plano-concave lens, at 

 the distance of the diameter of the sphere of curvature ; 

 and for a double-concave, in. the centre of that sphere. If 

 a lens be convex on one side and concave on the other, 

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