LIGHT AND SOUND. 



the poker, an inverted image is seen, and within 

 and without that, an erect image. 



If the medium on which rays of light fall is 

 bounded by two parallel faces, the rays, after pass- 

 ing through the plate, will be parallel to their 

 direction before entering it, since the refraction 

 at the one surface must be equal and opposite 

 to that at the other. But if light falls on a re- 

 fracting prism, it emerges in quite a different 

 direction. Let ABC be the prism, say of glass, 



Fig. 12. 



on which the ray DE falls ; the direction within 

 the prism is not EF, but EG, nearer the line 

 EH, which is perpendicular to AB. At the 

 second face, the ray is bent from the perpendicular 

 GH, and takes the direction GL. By the refrac- 

 tion at both faces, the ray has been bent from the 

 direction DF into GL, and the angle between 

 these directions is called the deviation of the ray, 

 which is always towards the thick part of the prism, 

 and is proved, by a simple mathematical investiga- 

 tion, to be the least possible when the incident 

 and emergent rays make equal angles with the 

 faces of the prism. 



If the refracting medium be bounded by curved 

 faces, it is called a lens, and may have one or 

 other of the following forms : A is called a double 

 convex lens ; B, convexo-plane, or plano-convex, 



according as the light falls first on the one 

 side or the other. C is a double concave ; D, 

 plano-concave ; E, a meniscus ; and F, a concavo- 

 convex. They may be divided into two classes, 

 according as they are thickest or thinnest in the 

 middle ; and they all, like the prism, deflect a ray of 

 light towards the thick part. Therefore, a parallel 

 beam of light, falling on one of these lenses, will be 

 rendered converging or diverging, according as the 

 lens belongs to the first or the second class. In fig. 

 14, the parallel rays are bent within the lens in the 

 direction of the point A, but on emerging from the 

 lens they are further bent, so that they converge 

 to a nearer point, B. In the lower figure, the rays 

 within the concave lens are bent as if they had 

 come from C, and on leaving the lens, they seem 

 to proceed from D. The points B and D are 

 called the foci for parallel rays, or the principal 

 foci of the lenses, and it is evident that B is a real, 



and D a virtual focus. The distance from the 

 centre of the lens to the principal focus is called 

 its focal length, and if the curvature of the two 



Fig. 14. 



faces is the same, and both faces are spherical, 

 this focus is at the centre of the sphere. As in 

 reflection at a spherical surface, so likewise in re- 

 fraction, rays at all distances from the axis are not 

 brought accurately to one point, those falling on 

 the lens fnear the edge being brought sooner to 

 a focus than those near the axis. This drawing 

 out of the focus from a point into a line is called 

 the aberration of the lens, and might be partly 

 remedied by covering up the parts near the edge, 

 or those near the centre, with a stop or diaphragm. 

 If a pencil of parallel rays falls obliquely on a lens, 

 it is still brought very nearly to a focus, which is 



Fig- IS- 



thus found. Take that ray, AB, of the oblique 

 pencil which passes through C, the centre of the 

 ens ; the focus of the pencil lies in this line, at a 

 distance, CF, from the centre equal to the principal 

 : ocal length. 



The effect of a lens thick in the middle, or con- 

 vex, being to render a parallel beam convergent, 

 t is easy to see that if a beam be already convergent, 

 a convex lens will make it still more convergent ; 

 and if the beam be divergent, the same lens will 

 diminish its divergency. 



To understand how images are formed by lenses, 

 let us take a double convex lens, and place an 

 object, ABC, farther from it than F, its principal 

 focus ; all the rays coming from B, and falling on 

 the lens, are refracted to some point, b, on the axis, 

 neglecting the aberration, so that at b an image of 

 the point B is formed. To find the image of A, 

 draw a line from A through the centre of the 

 lens, and the focus required is somewhere on 

 this line, as at <z, so that the rays falling on 



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