THE DOG AND THE SHADOW. 



lake or river, viewed by an observer (fig., page 193,) stationed 

 .at a considerable distance on the opposite side, are very vivid, the 

 rays which produce vision in that case being those which fall with 

 great obliquity on the water. 



Since it appears, however, that when the angle of incidence is 

 60, and, therefore, the obliquity 30, less than a fifteenth of the 

 entire number of incident rays are reflected by the water, the 

 image must become fifteen times less vivid. If, therefore, the 

 observer approach the opposite bank, as he may do in a boat, its 

 image reflected in the water will be less and less vivid ; or the 

 same effect may be produced in some cases by taking a more 

 elevated position, without changing his distance. Indeed this 

 will give a more accurate result than the former, inasmuch as the 

 change of distance of the eye of the observer from the point of 

 reflection ought strictly to be taken into the account. 



If the observer assume such a position, either by increasing his 

 elevation or by diminishing his distance, that the angle of inci- 

 dence shall be reduced to 30, and, therefore, the obliquity to 60, 

 no more than eighteen rays in a thousand will reach the eye ; and 

 if the obliquity be still further diminished, the number of reflected 

 rays will be much more inconsiderable. 



Thus, by gradually diminishing the obliquity of the incident 

 rays by the change of position of the observer, the reflected 

 image, at first vivid, will be gradually more and more faint, until 

 at length it will cease to be perceptible. 



4. If a person look down into still water, over the bulwark of 

 a vessel, he will not perceive any reflected image of his person ; 

 but if he lean over the gunwale of a boat, at a much less dis- 

 tance from the surface, he will perceive a faint reflection of his 

 person under certain circumstances. The cause of this is easily 

 explained. 



The image formed by reflection is as far behind the reflecting 

 surface as the object is before it, and the intensity of the light 

 proceeding from such an image decreases in the same proportion 

 as the square of its distance from the observer increases. When, 

 therefore, the observer looks over the bulwark of a vessel, the 

 distance of his face from the surface of the water being, for 

 example, 12 feet, the distance of the image formed by reflection is 

 24 feet. The obliquity of the pencils which, proceeding from his 

 face, are reflected by the water is very small, the rays being nearly 

 perpendicular. Not more, therefore, than about two in every 

 hundred of such rays are reflected to his eye, and these diverge 

 from an image at 24 feet distance. The intensity of such reflected 

 light is, therefore, insufficient to produce a sensible effect on the 

 retina. 



o 2 195 



