LIGHT AND SOUND. 



looked into from the other side. Let ACB be a 

 section of such a surface through its centre, O. 

 AB is called the aperture of the mirror ; C, the 



Fig. 6. 



centre of the aperture ; O, the centre of curvature ; 

 CO, the radius ; and the line COP the axis. If 

 PM be a ray coming from the luminous point, P, 

 since MO is perpendicular to the surface at M, it 

 will be reflected in MQ, making the angle OMQ 

 equal to the angle PMO. Another ray coming 

 from P, and striking the mirror at a different 

 point, as N, will not be reflected exactly to Q, so 

 that there is no exact image formed of the point 

 P. The image is drawn out into a line, in which, 

 however, one point is brighter than the rest : that 

 point, namely, which is formed by rays striking 

 near C. The farther the luminous point, P, is 

 from the mirror, the nearer is this bright point 

 to the middle of CO ; and when P is so far off 

 that the rays coming from it may be considered to 

 have lost their diverging character, the bright 

 point is exactly half-way between C and O. This 

 point is therefore called the principal focus of the 

 mirror, and the distance, CQ, is then called the 

 focal length. It is clearly equal to half the radius. 

 The indistinctness of the image, caused by all the 

 rays not being brought accurately to one focus, is 

 called the aberration of the mirror. 



To explain the formation of images by such a 

 mirror, let PQR be the object, AB the mirror, and 

 O its centre. The brightest point on the image of 



Fig. 7. 



Q is g, rather nearer the centre, O, than F is, the 

 middle of CO. Also for P, its principal image is 

 in the line POM, at p, between O and/i, the 

 middle of OM. Proceeding in this way for all 

 points of the object, FOR, we find the image, pqr, 

 which we thus see is diminished and inverted. 



It is to be observed also that the reflected 

 rays actually pass through the image, which is 

 called a real one ; whereas, with a plane mirror, 

 the reflected rays do not pass through the image, 

 which is consequently called a virtual one. If the 

 points P, Q, R, are in a straight line, their images, 

 p, g, r, are not, so that the image of the object is 

 curved. Again, of all the rays coming from P, it 



is only those striking the mirror in the immediate 

 neighbourhood of M that are reflected to p, the 

 rays falling more- obliquely being reflected to 

 different points. This produces confusion in the 

 image, which, however, may be obviated by inter- 

 posing a diaphragm, XY, to cut off all the indirect 



! pencils. If we consider pqr as a small object, then 

 PQR is its image, which is real, magnified and 



1 inverted, but is affected by the aberration, curva- 

 ture, and confusion, as before. If the sun is 

 the object in front of the mirror, then a small 



but bright image is formed at the principal focus. 



' This explains the use of such mirrors as burning- 

 glasses, where a parallel beam of light is made 

 to converge to a focus. If a light is placed in 

 the focus, then its rays are reflected in a parallel 

 beam, and consequently such reflectors are used 

 for lamps of coaches and light -houses. For convex 

 spherical mirrors, the image is always virtual and 

 diminished. 



REFRACTION OF LIGHT. 



It has been already mentioned that as long 

 as rays of light are in the same medium, they 

 travel in straight lines. If, however, the rays sud- 

 denly change their medium for instance, if they 

 enter water from air their direction is suddenly 

 changed, or they are refracted, unless they strike 

 the bounding surface perpendicularly. In the 

 diagram, let AB 

 represent the ray 

 travelling in air, 

 and meeting the 

 surface, CD, of the 

 water at B. Its 

 direction in the 

 water is not BE, 

 in the same line 

 with AB, but BF, 

 nearer the perpen- 

 dicular, GBH. If 

 we mark off equal 

 lengths, BA, BK, 

 in the two direc- 

 tions, and draw 

 AG, LK, at right 

 angles to GH, then 

 the exact law is expressed by saying that at what- 

 ever angle AB strikes the surface, the ratio of AG 

 to KL is always the same. This constant ratio is 

 called the index of refraction for the two media, 

 and in the case of air and water is very nearly f , or 

 LK is three-quarters of AG. If we suppose the 

 motion of the ray reversed that is, if it proceeds 

 from water to air it travels in the direction FBA, 

 so that it is bent or refracted away from the per- 

 pendicular, GH. Thus the refraction is towards 

 the perpendicular to the common surface if the 

 second medium is the denser of the two, but away 

 from it if less dense. Generally speaking, the 

 greater the difference of density of the two media, 

 the greater is the index of refraction. And if we 

 take each medium with a vacuum, the index of 

 refraction is then called the absolute refractive 

 index. Inflammable media, if transparent, have 

 high refractive powers ; and Newton, observing 

 the high refractive index of the diamond, conjec- 

 tured that it would prove to be inflammable a 

 conjecture which has been subsequently verified. 



The following simple experiments are well 



