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from the table of natural sines this shows the critical angle 

 for glass to be 41°, or, to be very exact, 41° 48'. 



We have seen that, when parallel light passes through a 

 convex lens, its emergent rays are brought to a point at a 

 nearer or greater distance from the lens, according to the 

 intensity of the curve of the side or sides of the lens. This 

 point is called the focus of the lens, and it is the distance of 

 this point from the lens which determines its magnifying 

 power. For the calculations of the optician the distance of 

 distinct vision has been taken in this country as 10 inches. 

 If, then, the focus is one inch distant from the lens, its mag- 

 nifying power is said to be 10 times ; if half an inch distant, 

 20 times; and if a quarter inch distant, 40 times, and so on, 

 the 10 inches of distinct vision being divided by the focal 

 length of the lens. 



When the practical optician came to construct convex 

 lenses, he found himself confronted by two serious difficulties 

 in obtaining a clear and distinct image of the object seen 

 through the lens. The first of these was inherent in the form 

 of the lens, and received the name of spherical aberration ; 

 and the other was in the composition of light, and received 

 the name of chromatic aberration. 



Spherical Aberration. — We have said that the emergent 

 rays of light, after passing through a convex lens, were united 

 in a point called the focus. This is not literally the case, for, 

 owing to the form of the lens, the rays which pass through 

 near the periphery of the lens are brought to a focus nearer 

 the lens than those which pass through nearer the centre of 

 the lens. The effect of this was to give a blurred view of the 

 object. To remedy this defect in some measure, the periph- 

 eral rays were stopped out, and only those passing through 

 near the centre of the lens were utilised. This is still what 

 is done in the case of many pocket-lenses, such as that known 

 as the " Coddington." This form was, however, of no use for 

 the purposes of the higher optical instruments. Formerly for 

 the construction of lenses the opticians had at their command 

 only two materials — crown-glass and flint-glass. As both 

 the refractive power and the dispersive power of these two 

 kinds of glass are different, the opticians, by a judicious com- 

 bination of different forms of lenses made from these glasses, 



